The television personality, 56, made headlines about a month ago when he offered intense criticism of Markle and Prince Harry's claims made against the royal family in their tell-all interview with Oprah Winfrey.
The fallout from his criticism included him storming off the set of "Good Morning Britain" after being called out for his constantly negative view of the Duchess before it was announced that he would not return to the daytime program.
As the drama surrounding the incident winds down, Morgan has revealed what he would say to Markle, 39, should they speak.
"I would say to Meghan Markle, ‘Look, sit down with me with your husband for an equally long interview ... and let me ask you more difficult questions about all your claims," he told Extra. "But let me ask you a wider question, which is this: If you hate the royal family that much, why do you keep your royal titles? Why do you keep calling yourself the Duke and Duchess of Sussex? Why would you do that if it's just not to make millions and millions of dollars?"
He added: "And playing the victim as you do is, frankly, nauseating."
After the royals' interview, Morgan said on air that he did not believe the claims they made, including accusations of racism by the royal family and the reveal that Markle faced suicidal thoughts due to intense media coverage.
Complaints were lobbied at "Good Morning Britain" over his comments, and it was reported that Markle was among those to do so -- reportedly even calling an ITV executive to discuss the matter.
Morgan said he wasn't aware that Markle had contacted his employer until after he left the show.
"It was certainly a very interesting revelation from where I sit because clearly, she was trying to put huge pressure on my bosses to take action against me," he said.
Furthermore, he said the complaints came from "an online mob" who he accused of "abusing" his sons and "issuing death threats to them."
"The idea that my sons had to be targeted by so-called liberals in a way that was threatening to them, abusive and death threats and so on is completely disgusting," Morgan said.
He also addressed the drama surrounding Osbourne, who sparred on-air with co-host Sheryl Underwood as she tried to explain why Morgan's views could be considered racist, and why Osbourne's support could be considered enabling.
"Look at what happened to Sharon on 'The Talk' for defending me and my right to have an opinion, even though she made it clear that she didn't agree with everything I was saying," he said. "She was then targeted by Sheryl Underwood on 'The Talk,' and she was accused of supporting someone who had said racist things."
Morgan insisted that his disbelieving Markle isn't racist and that Underwood -- not Osbourne -- should be the co-host to have lost her daytime show job "for falsely accusing [him] of racism."
The media personality said messages from members of the royal family have been "communicated" to him, thanking him for his support, but he refused to disclose who it was that offered their thanks and whether they were senior members of the family.
"The only thing I'd have done differently -- I wouldn't have walked out in the middle of the show the way that I did," he added. "I don't think Americans realize it was only for a few minutes and I went back in and did two more hours of the show."