Trump pressing DeSantis to name Lara Trump as Rubio's Senate successor: source

President-elect Trump named Rubio as his pick for secretary of state last month, leaving DeSantis the decision to name a successor to the position. DeSantis said last month that he will likely name his pick for the seat by early January. 

Speculation has mounted in recent weeks that Lara Trump is a likely choice for the role, as Republican lawmakers such as Sens. Rick Scott, Lindsey Graham, Katie Britt and Rep. Anna Paulina Luna of Florida voiced support for her filling Rubio's Senate shoes. Lara Trump is married to the 45th president's son, Eric Trump, and co-chaired the RNC amid the 2024 presidential campaign. 

If Rubio is confirmed as the U.S.' next secretary of state, his successor would serve in the Senate for two years before the seat is up for election again in 2026. 

Amid speculation over Rubio's potential replacement, Lara Trump announced this week that she will step down as co-chair of the Republican National Committee (RNC) after serving in the position throughout the presidential campaign. She explained in a social media post that she fulfilled three goals she sought as GOP co-chair, and would "formally step down from the RNC at our next meeting." 

"It is something I would seriously consider," she told The Associated Press. "If I'm being completely transparent, I don't know exactly what that would look like. And I certainly want to get all of the information possible if that is something that's real for me. But yeah, I would 100% consider it."

She additionally told Fox News' Sean Hannity last month that she "would love to serve the people of Florida" and "would love to consider" filling the seat if asked.

Fox News Digital's Christina Shaw and Alex Nitzberg contributed to this report.