President-elect Donald J. Trump is expected to name Senator Marco Rubio of Florida as his secretary of state, three people familiar with his thinking said on Monday, as Mr. Trump moves rapidly to fill out his foreign policy and national security team.

Mr. Trump could still change his mind at the last minute, the people said, but appeared to have settled on Mr. Rubio, whom he also considered when choosing his running mate this year.

Mr. Rubio was elected to the Senate in 2010, and has staked out a position as a foreign policy hawk, taking hard lines on China and Iran in particular.

He initially found himself at odds with those Republicans who were more skeptical about interventions abroad, but he has also echoed Mr. Trump more recently on issues like Russia’s war against Ukraine, saying that the conflict has reached a stalemate and “needs to be brought to a conclusion.”

Mr. Rubio was a loyal surrogate for Mr. Trump during the campaign even after being passed over as the vice-presidential pick.

A spokesman for Mr. Rubio declined to comment, and a spokesman for Mr. Trump did not immediately respond to a request for comment.

Mr. Trump has made his choice for a number of other national security roles. He has selected Representative Michael Waltz, Republican of Florida, to be his national security adviser, and Representative Elise Stefanik, Republican of New York, to be ambassador to the United Nations.

Mr. Rubio was he was first elected to the Senate in 2010 as part of a new generation of conservative Tea Party leaders. But some conservatives considered him wobbly on immigration, an issue that caused him political problems when he ran for the Republican presidential nomination in 2016 against Mr. Trump and others.

During that campaign, Mr. Trump belittled him as “Little Marco,” and Mr. Rubio responded with acerbic attacks.

But after Mr. Trump’s 2016 victory, Mr. Rubio went on to patch things up with him, serving as an informal foreign policy adviser and helping to prepare him for his first debate against President Biden in 2020.

Under Florida law, Gov. Ron DeSantis can temporarily appoint a replacement to Mr. Rubio’s seat who will serve in the Senate until the next regularly scheduled general election is held. After last week’s elections, Republicans are set to hold at least 52 seats in the chamber.

Catie Edmondson contributed reporting.