Labour, the Conservatives and the Liberal Democrats have held a series of meetings to consider the possibility of a live programme featuring Gordon Brown, David Cameron and Nick Clegg, The Times reports.
Advisers to the parties are said to believe that Frost, who famously interviewed former US President Richard Nixon in 1977, would be an unbiased chair.
A Conservative Party spokesman said: "David Cameron has always called for a television debate; he was the first to do so. He has asked for one at the dispatch box and also in a letter to Gordon Brown."
A Liberal Democrat spokesman added: "Nick is very eager to take part in this type of debate. But it is all about whether Gordon Brown agrees to appear.
"We have attended meetings over the recess with broadcasters who are interested. We very much hope that this is something we can make happen."
The rules governing any live debate and the details of its format are yet to be agreed, while it has been suggested that all channels, radio stations and websites would have access to a live feed.
> ITV considers own live leaders debate