RTE has insisted Ryan Tubridy's 2fm show is not under threat, in spite of losing 110,000 listeners.
The station made the comment as Communications Minister Pat Rabbitte branded the salaries of its stars "excessive".
Claims had circulated that the host of The Tubridy Show was told to improve his ratings or he would be replaced in the 9-11am weekday slot.
One report stated that, at a crunch meeting with RTE management, the Late Late Show host was given three months to boost his listenership.
Since he took over from the late Gerry Ryan last year, Tubridy's audience has fallen by 110,000, according to JNLR survey figures published last month.
But RTE insisted it is not looking to replace the 38-year-old in the key morning slot.
Rubbishing the speculation, a spokesman told the Herald everyone at 2fm, including Ryan, "recognise the challenges of the months ahead".
However, he pointed to recent positive comments by RTE managing director Clare Duignan and John McMahon, the head of 2fm, before adding "the show is working, it has found its rhythm, and now it's about making sure more listeners hear it".
Meanwhile, Mr Rabbitte told a Sunday newspaper the broadcaster must reduce its spending to bring it in line with revenues.
The station spent €4.7m more than it took in last year, following on from losses of €16.5m in 2009.
"RTE can't go on incurring the kind of annual deficit that it is incurring and their costs simply have to be brought under control," he said.
Mr Rabbitte, the Minister for Communications, Energy & Natural Resources, said the situation can't exist in which RTE is "allowed to run up a big deficit every year".
"I've told the Director General they have to get it under control," he told the newspaper.
Mr Rabbitte, whose remit includes RTE, indicated the station's highest earners like Tubridy, Pat Kenny and Marian Finucane, will pay the most.
"(As) far as the Government is concerned, we expect those earning most to contribute most to the savings programme."
The Dublin South West TD said no one is "indispensable", adding he is "damn sure" RTE has the talent "buried there somewhere" to take over.
He also said director general Noel Curran was committed to slashing the salaries of the top RTE presenters by 30pc when their contracts come up for renewal.
Mr Kenny was paid €950,976 in 2008, while Ms Finucane received €570,000.
Tubridy earned €533,000 but this figure is likely to have increased substantially since he took over the Late Late Show in 2009.
He is currently acting as a summer weekend replacement for Graham Norton on BBC Radio 2 for an eight-week stint.
His 2fm show is to get a shake-up in September, with new producer Paul Russell lined up to take over the programme.
Mr Russell also worked with Tubridy on his Radio 1 show, which eventually became one of the station's most successful.
RTE head of radio Clare Duignan recently defended the JNLR figures, saying the Tubridy show had now found its "rhythm".
Pat Stacey, Page 15