“I’m quite confident, very confident in fact, that I’ll be able to win that vote of no confidence,” he told Sky News.
Scottish National Party leader Yousaf ended an alliance with the Scottish Greens after a dispute over a decision to scrap a climate change emissions reduction target last week.
The Scottish arm of the Conservative Party that governs Britain then said it would seek to topple Yousaf with a no-confidence motion, calling him a “lame duck”.
His position now hangs on a knife-edge vote after almost all other parties, including his former coalition partners, said they would vote against him.
With the Conservatives, Labour, Greens and Liberal Democrats all indicating they have no confidence in Yousaf, he would need the support of Ash Regan - a one-time leadership rival to Yousaf who acrimoniously left the SNP last year - to cling on as first minister.
If Yousaf lost, parliament would have 28 days to choose a new first minister before an election was forced.