Claire Byrne has been described as a shoo-in to take over Sean O'Rourke's old radio slot in September.
An RTE source said the TV and radio presenter is top of the list to take the reins of the weekday Today programme, which is currently being helmed by Sarah McInerney.
While the former Newstalk anchor is being praised by critics for her no-nonsense approach with government ministers, the source said it is "unlikely but not impossible" that she will keep the job.
"The Today programme is one of the biggest programmes in the radio schedule and, to be honest, Claire is a shoo-in," the source added.
"Nothing is set in stone, but right now Claire is a bit like Liverpool in the Premier League.
"Sarah has done a great job in the interim and has made all the right moves, but Claire is definitely the front-runner.
"Miriam O'Callaghan is still in the conversation, but she's so heavily invested in Prime Time that it would be a big ask for her to do both."
One bookie has slashed Byrne's odds from 4/1 to 4/6 favourite. McInerney is 2/1 to stay put, while O'Callaghan has drifted to 6/1.
O'Rourke spent seven years as the Today host, taking over from Pat Kenny in 2013 following a distinguished career in print and broadcast journalism.
Since his departure in May, speculation has run wild as to who will succeed him.
Ivan Yates' decision to leave Newstalk later this month has set tongues wagging, with some suggesting he might be in the running.
However, another source said that while negotiations had reached an advanced stage, a final decision would not be made for some weeks yet.
"There are so many big changes coming up in RTE that everything is being done quietly and carefully," the source said.
"So many talented people are in the mix for top positions that it's important Sean's successor is chosen the right way without offending anyone.
"A final decision will be made in a couple of weeks, but an announcement won't be made until closer to September."
The appointment is part of a major reshuffle and rebrand of various RTE current affairs shows.
With David McCullough joining Caitriona Perry on the Six One News, a slot has been left vacant alongside O'Callaghan on Prime Time.
It is understood executives are keen to pair O'Callaghan with another strong female lead on the news programme.
"With David moving to the Six One, there's a chance to give Prime Time a bit of a shake-up," the source said.
"The early conversations have been about that. Like what happened with Caitriona Perry and Keelin Shanley, it will be an all-female affair.
"You would have to say that Sarah McInerney would be part of that conversation, as would Mary Wilson and Sharon Ni Bheolain.
"But again, that decision won't be made until after the Today show is unveiled."