Claire Byrne has been described as a "shoo-in" to take over Sean O'Rourke's old radio slot in September.
An RTÉ source said the TV and radio presenter was 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 has been praised by critics for her no-nonsense approach with Government ministers, the source said it was "unlikely but not impossible" that she would 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 frontrunner.
"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."
BoyleSports has slashed Byrne's odds from 4/1 to 4/6 favourite. McInerney is 2/1, while O'Callaghan has drifted to 6/1.
O'Rourke spent seven years as the 'Today' host, taking over from Pat Kenny in 2013.
Since his departure in May, speculation has run wild as to who will succeed him.
Ivan Yates's 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 were at an advanced stage, a final decision would not be made for some weeks yet.
"There are so many big changes coming up in RTÉ 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 RTÉ current affairs shows.
With David McCullagh joining Caitríona 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 female lead on the 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.