David Davis has said he would be very happy to make rival David Cameron his deputy if he wins the contest to become party leader.
Mr Davis said it would be his last chance to stand for the job
Speaking in an interview with Sky News, broadcast on Monday, he said Mr Cameron would have a "very, very big place in any shadow cabinet I lead".
He added that, at 56, it would most likely be his last bid for the job.
But Mr Cameron said he had not "promised anybody any jobs in the shadow cabinet".
'Mountain to climb'
Earlier, Mr Davis said: "If I win David will have a very, very big place in any shadow cabinet I lead.
"One of the newspaper journalists yesterday was saying we should be the deputy leader in each other's team.
"From my point of view, I would be very happy to have him as deputy leader."
Mr Cameron promised a shadow cabinet 'of all the talents'
When asked if he would stand for the leadership again, Mr Davis replied: "Whoever wins this time has a very good chance of winning the next general election and as a result that would not be until after my retirement."
The shadow home secretary has admitted he faces "a mountain to climb" to overtake Mr Cameron in the next three weeks.
One comparison between the two men has pitched Mr Davis as the Bash Street Kids and Mr Cameron as Little Lord Fauntleroy.
Mr Davis said he thought that tag unfair to his rival but said his own background had shaped his desire to be the "champion of the least well off".
In another interview with Sky News, Mr Cameron praised Mr Davis's "incredible talents" and his work as shadow home secretary.
The shadow education secretary added that his rival had "given a lot to the Conservative Party and has got a lot more to give".
Mr Cameron promised a "shadow cabinet of all the talents", from all wings of the party and age groups, should he win the contest.
He launched his six-week tour of the country in Birmingham, the scene of weekend riots.
Mr Cameron on Sunday used a speech at an inner city regeneration project in Birmingham to explain why the Conservatives needed to win back support in cities to regain power.
Earlier, he said a "national school leavers programme", similar to National Service, should be reintroduced in Britain to help build communities against the threat of terrorism.
He said the country lacked the "shared experiences" brought about by schemes such as National Service.
Mr Cameron, who has not ruled out making the programme compulsory, suggested it could be like the Peace Corp set up by US President John F Kennedy.
Ballot papers for the 300,000 Tory members who will decide the contest are being sent out next week.
Nine hustings, where the candidates appear head to head, will be held around the country before polls close on 5 December.