Yvette Cooper and Liz Kendall have denied reports that Lord Mandelson tried to persuade the three mainstream Labour leadership candidates to quit the leadership contest and force the party to stop the election.
The move by the former politician and 1997 election campaign leader highlights maneuvers within the party to stop Mr Corbyn winning the election.
Ms Cooper said she had not been approached directly by the Labour peer, she was unaware if her campaign team had been contacted.
Ms Kendall insisted that neither she nor her office had spoken to him.
Labour heavyweight Lord Mandelson has praised Ed Miliband for pledging a possible referendum on EU membership.
The former Business Secretary and EU Commissioner told BBC Radio 4's Today programme:
"I think it will be seen over time as quite a game-changer for Ed Miliband. I think he's shown judgment and courage. I think he's gone out and made the political weather on a major issue and I think as a result it will strengthen him and help him win the next election."
However, the Labour peer admitted that for most voters Europe was "not the major deciding issue for them when it comes to deciding how they're going to vote in a general election".
Prime Minister David Cameron spoke to former European Commissioner and ex-Labour Business Secretary Lord Mandelson after bumping into him at the World Economic Forum in Davos.
Ed Miliband should hold his nerve and not be "dragged along by the Ukip bandwagon" on Britain's membership of the European Union, former Labour minister and ex-European Commissioner Lord Mandelson told ITV News.
The Labour leader previously said he was against holding an in-out referendum under the terms proposed by Prime Minister David Cameron.
Lord Mandelson told Libby Wiener: "I think Ed Miliband is right to stand his ground but also to say that if there is in the future a need for, circumstances arising that require a referendum, then of course a Labour government would agree to that and put it to the British people".
Former European Commissioner Lord Mandelson has told ITV News Britain should not be "over-sensitive" after a European Commission vice-president said UK political leaders are "destroying the future" of Britons by adopting populist policies on immigration:
Lord Mandelson has said the Labour party would be "foolhardy" to offer any sort of in/out referendum on the EU - but said one might be needed to see if the public wanted to join a reformed single currency.
The former cabinet minister and EU trade commissioner said he did not believe David Cameron would commit to a public vote because for the Tories it would spell "political suicide by splitting them from top to tail.
"I do not think the Labour Party would be so foolhardy as to have a 'clear the air' referendum," he said.
But in five to 10 years, if the eurozone was reformed and there was a "gravitational pull of power, decision making and policy" among the member states that belonged to it, voters might want to "reconsider whether we want to join the core".
"It will not be for government or a political party or a combination of political parties to make that decision; it will be one for the British people," he added.
Former EU commissioner Lord Mandelson told the BBC Radio 4 Today programme that he expected Mr Hollande and Mrs Merkel to mount a renewed push for greater EU integration in order to shore up the eurozone.