Mr Gove, talking earlier than the vote on LBC, stated Ms Badenoch had “star high quality”.
He added: “Every little thing might align, it’s attainable. What we’ve seen on this race is that the extra folks see of Kemi, the extra impressed they’re.”
Mr Tugendhat, whose endorsement may even be keenly sought, stated he would take his time: “I’ll hearken to what they must say and I will be making my judgment later.”
Ms Badenoch praised Mr Tugendhat late on Monday night, hours after he was eradicated from the competition.
“And one closing factor earlier than bedtime,” Ms Badenoch tweeted. “Thanks and effectively executed to my good friend Tom Tugendhat on a well-fought marketing campaign.
“Like me, he loves our nation deeply and I do know he can be an asset to any future Conservative authorities.”