No, it's all media speculation and I'm sure Meghan herself pushing it. As Susan pointed out, the Governor can call a special election or he can make a temporary appointment to fill the seat until 2026, or he can fill the position himself. That very, very rarely happens as does the special election.
The media has also been running the story that the Gov. has blocked all calls from Meghan. So what does that tell us? If he appointed Markle, there would be an uproar among the public, GOP, and the Democrats. The media keeps up the BS that Markle's the darling of the Democrats....she's not. They are steering to the south of her, the public doesn't like her and......she has to lose the title, but still remains a member of the British Royal Family which can be used against her...among a ton of other issues.