Mr Trump voiced his support for Lara Trump and Michael Whatley, chair of North Carolina's Republican party.
His backing on Monday follows reports that he has grown frustrated with the RNC's current leadership.
The committee would vote for new leadership if its current head, Ronna McDaniel, steps down.
US media has reported that Ms McDaniel may leave her post after the South Carolina Republican primary, scheduled for 24 February.
The RNC as an organisation focuses on fundraising for the party and on getting Republicans out to vote.
As the frontrunner candidate for the Republican party in this year's election, Mr Trump's endorsement will likely have some influence among RNC members.
In a Monday evening statement, Mr Trump said Mr Whatley, who currently serves as the committee's general counsel, "has done a great job in his home state of North Carolina" and that he should be the RNC's next chair.
He also lauded Mr Whatley's commitment to "election integrity". Mr Whatley has previously championed the former president's baseless allegations of election fraud in the 2020 election.
For the role of RNC co-chair, Mr Trump said he endorses his "very talented" daughter-in-law Lara Trump, who is married to his son Eric.
"Lara is an extremely talented communicator and is dedicated to all that MAGA stands for," Mr Trump said.
Ms Trump has worked closely with the RNC in the past and is seen as an effective fundraiser by the committee.
Party rules mandate that there be one male and one female at the helm of the RNC.
The former president said he has also asked Chris LaCivita, the co-manager of his current presidential campaign, to take on the role of RNC's chief operating officer.
Politico reported that, should Mr Lacivita assume the role, he will still maintain his position as Mr Trump's co-campaign manager.
If Mr Trump's endorsements were to go ahead, it would mean his campaign would be aligned closely with the committee and its operations.
But his stamp of approval has not always been effective. Mr Whaley failed in his 2023 bid for co-chair despite a previous endorsement by Mr Trump.
The push for a change in leadership comes after disagreements between Mr Trump and Ms McDaniel, the current RNC chair, over the Republican primary debates ahead of this year's election. The former president has refused to participate in any of them.
The Washington Post previously reported that Mr Trump pushed Ms McDaniel to cancel the debates altogether, but she refused.
She has also faced pressure over the party's poor performance in recent elections and for lacklustre fundraising.
She was expected to serve in her role until 2025, but news of her possible resignation emerged after she met with Mr Trump in Mar-a-Lago last week.
At that meeting, Ms McDaniel told Mr Trump that she will do whatever is best for the party, including stepping down.
When the conservative Newsmax network asked Mr Trump last week if Ms McDaniel should resign, he replied: "I think she knows that, I think she understands that."
By Nadine Yousif