While asserting emphatically that the Senate has the constitutional authority to decide its own membership, Reid told NBC's "Meet the Press" that he is not shutting the door on Burris entirely.
"There's always room to negotiate," he said. Asked whether that means Reid is not saying "no" altogether to Burris serving, Reid responded, "That's right."
Burris, 71, appointed by Illinois Gov. Rod Blagojevich travels to Washington Monday and will attempt Tuesday to enter the Senate chamber to be sworn in. Burris has not been accused of wrongdoing but is considered "tainted" by many senators because he is Blagojevich's appointee.
The governor has been accused by federal authorities of offering to sell the appointment to the highest bidder, but he has not been indicted yet. Reid said Blagojevich is "obviously" corrupt.
"There is a cloud over Blagojevich and at this stage a cloud over the state of Illinois. They don't have a vote and ... as long as Blagojevich has done the appointing it's really a tainted appointment," Reid said on NBC's "Meet the Press."
Congress convenes on Tuesday, and the belief is that Burris, in all probability, will not be seated next week.
"We determine who sits in the Senate and the House determines who sits in the House. So there's clearly legal authority for us to do whatever we want to and this goes back generations," Reid said.
It is unclear if Burris now stands a better chance of becoming a senator with Reid's softened tone, but the leader said he will meet with the chamber's top Republican on Monday evening to talk about what to do about Burris.
Still Democratic aides told FOX News it is highly unlikely Burris will be permitted entry into the Senate chamber Tuesday.
"This is still a tainted appointment, and Burris is not likely to show up with a signed certificate. If he doesn't have that, he's not going to be a senator," said one senior Senate Democratic leadership aide.
The certificate of appointment must bear the signatures of both the governor and the secretary of state. Secretary of State Jesse White has refused to sign the document because of the allegations of corruption against the governor.
Should the Illinois Supreme Court force White to sign the document, a move Burris is seeking, Burris would be allowed on the Senate floor. Reid or some other Democrat would then have to object to Burris being seated and call up a resolution that would send his credentials to the Rules Committee pending an investigation.
That move could buy enough time for Democrats in the Illinois Legislature to impeach the governor, a move that some say would nullify the Burris appointment.
Reid and his deputy, Illinois senior Sen. Dick Durbin, are also to sit down with Burris on Wednesday. But the Democratic leadership aide said not to take the meeting as a hopeful sign for Burris right now. "There's a reason the meeting is happening Wednesday. If they were serious about seating him now, the meeting would be on Monday or Tuesday," the aide said.
If the Senate refuses to seat Burris, his attorney said senators will have a legal challenge on their hands.
"We think there is clear precedent, there is no question with respect to the law. While I certainly do respect Majority Leader Reid, I think that his legal analysis is way off," attorney Tim Wright told FOX News.
Wright warned that the Senate is limited by "Powell v. McCormack," a Supreme Court decision that said the House was wrong to deny a duly-elected congressman a seat based on alleged impropriety of that member.
Wright said that Burris has done nothing wrong and that any move to block Burris from being seated would represent "the tyranny of the majority."
Wright added that hopefully when the Senate meets Tuesday, Burris will be given the oath of office.
"If that's not the case I believe our recourse will be in the federal courts," he said.
Reid said he doesn't want to close off any possibility for Burris to serve, noting that if Blagojevich is impeached and Lt. Gov. Pat Quinn becomes governor, he could appoint Burris.
Some have suggested that Burris could be seated provisionally, as has been done in the past, pending an investigation by the Rules Committee.
In 1996 Sen. Mary Landrieu, D-La., took her seat as the Senate looked into a recount battle in her state. But Durbin appeared to shut the door on that idea, noting the Louisiana case concerned a recount battle.
"I don't believe that will happen," Durbin told ABC's "This Week."
"He's making all of this up. I had a conversation with him, I don't remember what was in that conversation other than the generalities ... I didn't tell him who not to appoint," he said.
Reid added that Jackson Jr. "is somebody that I think would be a good senator."
Reid said the dispute is not about racial politics, adding, "Anyone to suggest anything racial is part of the Blagojevich spin."
"There is no question about race," Durbin said. "When we said at the beginning, Democratic senators said, we are not going to seat an appointment by Blagojevich, it was before he'd chosen anyone, black, white, or brown."
FOX News' Trish Turner and The Associated Press contributed to this report.