Former foreign minister Johnson is front-runner in the competition with Hunt, the current foreign minister, to be next leader of the Conservative Party and prime minister.
"Of course I would love to have Boris in my cabinet," Hunt told an audience of Conservative Party members at a hustings event in Exeter, southwest England.
"Boris is someone of enormous talent ... he should always have a very big role in taking things forward."Hunt also said he would serve Johnson if Johnson won the contest, adding: "I love my current job."