In a typically vociferous interview, the outspoken Ryanair boss told the €570,000-a-year weekend radio presenter she got too many days off.
Marian -- who earns €50 a minute on air -- enjoyed a two-month break from the station earlier this year.
O'Leary told her he would cut her holidays to four weeks.
That would go for stars such as Pat Kenny, Ryan Tubridy and Gerry Ryan too. He said that if he were in charge at Montrose the holiday policy would change drastically.
"In RTE, you could forget about your long holidays, four weeks per year, and if you didn't like it you could bugger off and get a job in the public sector," he said.
Finucane's salary came under the spotlight when it was revealed earlier this year that the presenter was earning €47.50 per minute for her four hours on the air weekly. But the presenter made no response when O'Leary took RTE contracts to task.
O'Leary, who described himself as "one of the biggest tax-payers in the country", also sensationally revealed that he had turned down an approach from the BBC to front hit show The Apprentice because he had no interest in "personal publicity".
"I said no because I think that it's too much of a distraction," he said. "And despite all appearances to the contrary, I've no interest in personal publicity.
"I do PR for Ryanair. I don't frankly want or need the publicity that comes from doing The Apprentice or those kind of gigs."
O'Leary was in warrior mode during his interview with Finucane on Saturday as he launched tirade after tirade of abuse -- with the Government the predominant target.
The business guru saved his most ferocious attack for former Taoiseach Bertie Ahern, referring to him as a "feckless ditherer".
"We elected Bertie Ahern three times in a row when it was clear that all he was doing was pandering to the trade unions and buying off the vested interests, anything at all.
"We deserve exactly what we get in this country at the moment because we elected that feckless ditherer three times.
"I don't think I'd say good morning to him and I don't think he'd say good morning to me either.
"The last time I met him, you could see the lips kind of getting all tight. I'd say he'd love to stick a knife in me if he could."