By Rene Marsh, Daniel Strauss and Alayna Treene, CNN

(CNN) — President-elect Donald Trump has privately encouraged Vivek Ramaswamy to consider an appointment to the US Senate seat recently vacated by Vice President-elect JD Vance if offered the position by Ohio Gov. Mike DeWine, according to a source familiar with the discussions.

Ramaswamy, a former biotech entrepreneur and 2024 Republican presidential candidate, already has been tapped by the president-elect to help lead the Department of Government Efficiency, an advisory board aimed at identifying cuts to the federal government.

Ramaswamy’s preference would be to focus on his role with DOGE and to run for Ohio governor in 2026, according to the source, but he is open to the Senate position if “everyone wants” him to assume the seat.

The encouragement by the president-elect comes as Ramaswamy met with DeWine, a Republican, over the weekend, according to a source familiar with the matter.

“Neither Governor DeWine nor our office has commented on any possible candidates for the pending appointment,” DeWine’s press secretary, Dan Tierney, told CNN in a statement.

Trump’s urging of Ramaswamy was first reported by The Washington Post. Politico first reported on the meeting between DeWine and Ramaswamy.

In a November post on social media, Ramaswamy said he was “withdrawing myself from consideration for the pending Senate appointment in Ohio,” vowing to “help” whoever DeWine selected to replace Vance.

Before being named to co-lead the DOGE effort, Ramaswamy had expressed interest in the vacancy, according to a GOP source familiar with the conversations.

The source also told CNN that Trump had raised Ramaswamy’s name with DeWine in recent weeks.

CNN previously reported that Ohio Lt. Gov. Jon Husted was a front-runner for the Senate vacancy. Husted, however, has long eyed a run for governor and has the opportunity to run in 2026 to succeed DeWine, who is term limited.

An Ohio GOP official told CNN the uncertainty over the jockeying for the Senate seat has contributed to Husted’s reluctance to accept an appointment. DeWine has yet to make an announcement, after telling reporters during a visit to Mar-a-Lago last week that he expected to “have an announcement probably next week.” The governor’s office hasn’t offered a more detailed timeline or said whether any last-minute discussions have caused a delay.

A source familiar with the matter told CNN that DeWine had not made a decision as of Wednesday morning.

The source added that Husted has been resisting getting the Senate appointment because of his interest in running for governor. There’s some talk about former Ohio GOP Party chair Jane Timken getting the nod but also concerns about her electability. And DeWine doesn’t want to pick a member of the House delegation given the narrow Republican majority, according to the source.

That has created an opening for Ramaswamy, but there’s resistance within the Ohio GOP over his possible appointment, according to the person familiar with the discussions.

DeWine has repeatedly stressed the importance of selecting someone who he believes “will be a worker” in the Senate, pointing to the 12 years he spent serving in the chamber.

“The US Senate rewards people who do hard work,” DeWine said last week. “It’s not just being on talk shows. It’s not just talking.”

CNN’s Jeff Zeleny and Manu Raju contributed to this report.

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