Yousaf's resignation was an option but a final decision had not yet been taken, BBC news reported citing a source close to the minister, Reuters reported.
Former Scottish National Party leader John Swinney has been approached by senior party figures to become an interim First Minister in the event of Yousaf being forced from office, the Times said, adding that Swinney is reluctant to step up because of personal circumstances.
Last week, Yousaf said he intended to fight a vote of no confidence called by political opponents after his decision to withdraw from a coalition agreement and try to run a minority government.
"I'm quite confident, very confident in fact, that I'll be able to win that vote of no confidence," he told Sky News on Friday.
If Yousaf loses, parliament would have 28 days to choose a new first minister before an election was forced.