Rory Stewart has told the BBC he is talking to his leadership rival Michael Gove “about combining forces”.
The BBC’s Norman Smith said that in a combined force, Mr Stewart would expect Mr Gove to support him.
Mr Gove’s team rejected the idea he would run a joint ticket with Mr Stewart at the top.
Another candidate will be eliminated from the race to be the next Tory leader in a third vote – due to take place on Wednesday evening.
The candidate who comes last will be knocked out of the race.
Surviving candidates will face further ballots until only two are left. Members of the Conservative Party will then be able to vote on the final two.
The BBC’s assistant political editor Norman Smith said it was understood that Mr Stewart would expect Mr Gove to support him.
Sources close to Mr Stewart said: “Clearly at some time people will need to combine teams. But any team that gets combined, Rory wants to lead.”
The BBC’s Laura Kuenssberg asked what the incentive would be for Mr Gove to give up his hopes of the top job, to put Mr Stewart at the top of the ticket
Speaking to the BBC’s Victoria Derbyshire programme, the international development secretary said that he and the environment secretary were talking about combining forces “because it’s clear that Boris is going into the last round”.
“And the question is ‘who is best placed to sit on stage with Boris Johnson, and who is best placed to ask the testing questions that need to be asked?”‘ he said.
The two men have argued for different approaches to Brexit – Michael Gove wants to negotiate a new deal with the EU, whereas Rory Stewart says this is unrealistic and wants to stick with the current deal.
When asked how they could compromise, Mr Stewart said: “If neither of us were prepared to budge on our analysis then we couldn’t combine as a team.”
Boris Johnson led the second vote securing 126 votes, ahead of Jeremy Hunt, Mr Gove, Mr Stewart, Sajid Javid and Dominic Raab.