Rory Stewart has told the BBC he is talking to his leadership rival Michael Gove “about combining forces”.
He said he needed to think about who was best placed to ask Boris Johnson “the testing questions”.
Acknowledging that the two men have different views on Brexit he said: “We would have to agree to compromise.”
Another candidate will be eliminated from the race to be the next Conservative 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 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.
Boris Johnson led the second vote securing 126 votes, ahead of Jeremy Hunt, Mr Gove, Mr Stewart, Sajid Javid and Dominic Raab.
Despite only just gaining the minimum number of votes yesterday to stay on the ballot paper, Home Secretary Mr Javid has said he is not planning to stand down from the leadership contest.
When asked if he was going to withdraw he said: “I was really pleased to get through yesterday and I’m looking forward to the challenges that lie ahead and making my case.”
Speaking earlier on Radio 4’s Today programme, Mr Stewart said he had received “some positive responses” from those who had previously supported eliminated candidate Dominic Raab.
Reflecting on the debate he tweeted: “Lesson from last night – my answer to a scratchy discourteous debate – shouldn’t have been to sit back – but to push more.”
During Tuesday’s TV debate, Mr Javid appeared to secure a commitment from the other candidates that they would approve an independent inquiry into Islamaphobia.
However there was less agreement on whether and how the UK could leave the EU by 31 October.
Ex-Foreign Secretary Mr Johnson said it would be “eminently feasible” but avoided offering an absolute guarantee.
Mr Gove and Mr Hunt said extra time might be needed. Mr Stewart said he would try to push through Theresa May’s Brexit deal which has already been rejected by MPs three times.
The debate was presented by Emily Maitlis who told the Today programme it was “a very bizarre thing to prepare for because up until 90 minutes before it started – you don’t which contenders will be in the race.”
She also said the candidates had, before the debate started, “all decided what boy band they were going to be” – a reference to the style and set up of the chairs.