This is a rush transcript from "Your World with Neil Cavuto," May 20, 2008. This copy may not be in its final form and may be updated.

NEIL CAVUTO, HOST: All right, Barack Obama secretly searching for a running mate, Bill Clinton secretly pushing for his wife to fill that slot — that is what TIME magazine is reporting at least.

What does former presidential candidate Michael Dukakis think of all of this? He joins me right now.

Governor, always good to see you. Thanks for coming.

MICHAEL DUKAKIS (D), FORMER MASSACHUSETTS GOVERNOR: Good to be back with you, Neil. Pleasure.

CAVUTO: Could it be 20 years, Governor? Twenty years, wow.

DUKAKIS: Can you believe that?

Video: Watch Neil's interview with Michael Dukakis

CAVUTO: Yes, wow.

DUKAKIS: Twenty years. Well, it`s been on long time, but there we are.

CAVUTO: There we are.

You know, there are a lot of folks looking at this race, saying that the running mate issue is going to be super-crucial for Barack Obama, that he needs to balance himself out. You had the Boston-Austin connection with Senator Bentsen at the time in Texas.

DUKAKIS: Right.

CAVUTO: Does he need to do a regional balancing act, or what do you think?

DUKAKIS: The first and most important question you have to ask yourself is, is this person that I`m about to pick qualified to be president of the United States if, God forbid, something happens to me? Everything else pales by comparison. That is the single most important question.

Now, regional balance and those kinds of things, helpful. Certainly, when I picked Lloyd Bentsen, one of the things I did right in the 1998 campaign...

(LAUGHTER)

DUKAKIS: And I did a lot of things wrong.

I picked somebody who came from Texas. But I did not pick him just because he came from Texas. I picked him because I don`t there`s anyone that doubted he would be a terrific president if something happened to me. Also, he was a guy with extensive Washington experience. I was a fellow that came out of state government. And I liked that as well.

CAVUTO: Right.

DUKAKIS: But, first and foremost, you have got to answer that question. Can this person be a first-rate president if something happens to me? Everything else is very, very unimportant by comparison.

CAVUTO: Well, the "everything else" part might be unimportant, but I always think, political cynic that I am, that the "everything else" becomes very important.

Do you think...

(CROSSTALK)

CAVUTO: What you think of the Hillary Clinton option, Governor, that, if this story is true, and Bill Clinton is pushing his wife as a running mate, what you think of that?

DUKAKIS: Well, let me say this.

Look, she should be on the list. I don`t think there`s any question about that. But he knows better than anybody that you have got to do this carefully and well. And you start by picking somebody, as he did — in his case, it was Warren Christopher — to head up the search for you, somebody in whom you have complete confidence.

You invited, Neil, suggestions from anywhere and everywhere. You look them over carefully. You begin to narrow the list down. For a variety of reasons, people tend to fall out. In some cases, you find out things about them that you didn`t know.

CAVUTO: Right. Right.

DUKAKIS: In other cases, they decide they don`t want to do it.

You get it down to a short list. In my case, it was four, John Glenn, Al Gore, Dick Gephardt, and Lloyd Bentsen. And then we put together volunteer investigating teams of lawyers and accountants that looked at every single thing they could about this particular person.

I interviewed them personally. Paul Brountas, the guy that headed up for the search for me, interviewed them personally. And, if you do it right — and it is hard to describe this, but, if you do it right, it inevitably leads to the right choice.

Clinton did that exact same process, in fact, asked us for the memo that Brountas gave me back in 1988, when he asked Warren Christopher to do this. And it led to — to Al Gore.

Now, from a regional standpoint, there was no reason at all to pick Gore, right?

CAVUTO: Right. Right.

DUKAKIS: I mean, they were in relatively small states next door to each other. But I will tell you, I thought picking Al Gore was a huge plus and a huge boost for Clinton. And that`s the way you have got to do it.

(CROSSTALK)

CAVUTO: I gotcha. Your point is well taken, Governor.

But on to this issue of likability. I mean, obviously, you liked Senator Bentsen, and he liked you. And we have had periods where bitter enemies have joined forces. John Kennedy and Lyndon Johnson comes to mind.

DUKAKIS: Yes. Yes.

CAVUTO: So, I am thinking, Barack Obama, no way in heck he would — he would put Hillary Clinton on that ticket. It just — with Bill there and all the baggage that comes with that, he just would not do it, right?

DUKAKIS: Well, I would not say that.

But I have just got to repeat to you, you have got to go through a process, got to be careful, got to be thoughtful. And, if he does it right, he will pick the right person. It could be Hillary. It could be somebody else.

CAVUTO: All right. But if that person were — if that person were Hillary Clinton — and, obviously, it would be meant to sort of calm both sides down — it has been a very divisive battle.

DUKAKIS: Yes.

CAVUTO: Is that a good way to decide it?

DUKAKIS: No. No. You shouldn`t pick somebody who will calm people down.

Look, the Democratic Party is going to be united. You know, Democrats have always been scrapping. One of my favorite Abraham Lincoln quotes, Neil, was when he was asked, way back in 19th century, why were the Democrats always fighting with each other?

And he said, you know, Democrats sound like cats fighting in the night, except, when you wake up in the morning, all they have been doing is making more Democrats.

(LAUGHTER)

DUKAKIS: And we have been making a lot of Democrats in this campaign, huge increases in registration and so on. I am not concerned about the fact that this party is going to come together.

What he`s got to do — what Obama has got to do is to carefully go through this process. And, if he does it and does right, he will pick the right person.

CAVUTO: Governor, always good seeing you. Thank you very much.

DUKAKIS: Good to talk with you.

CAVUTO: Governor Michael Dukakis. All right.

Content and Programming Copyright 2008 Fox News Network, Inc. ALL RIGHTS RESERVED. Transcription Copyright 2008 Voxant, Inc. (www.voxant.com), which takes sole responsibility for the accuracy of the transcription. ALL RIGHTS RESERVED. No license is granted to the user of this material except for the user's personal or internal use and, in such case, only one copy may be printed, nor shall user use any material for commercial purposes or in any fashion that may infringe upon Fox News Network, Inc.'s and Voxant Inc.'s copyrights or other proprietary rights or interests in the material. This is not a legal transcript for purposes of litigation.