The former Manchester United manager has been out of work since leaving a role at Old Trafford in December.
Various landing spots have been mooted for Mourinho since then.
He may have struggled to make the desired impact with United, but still landed three trophies in his debut campaign with the Red Devils.
Mourinho remains a man in demand and has seen a possible switch to Glasgow mooted heading into the summer, when the 56-year-old has stated that he intends to return to coaching.
Clarke, though, doubts that Scottish Premiership champions Celtic can pull off what would be a stunning coup.
He told reporters on the Parkhead speculation: “I did have a little grin.
“I’m not sure Jose would come to Scotland. He’d probably be looking to go to a more high-profile European league.
“And to somebody who is going to pay him a little bit closer to £12 million per year!”
Clarke worked alongside Mourinho during the latter’s first stint at Chelsea.
Considerable success was enjoyed together, including Premier League and League Cup successes.
It could be that their paths cross again at some point in the future.
It is, however, unlikely that Mourinho will be taking the reins at Celtic ahead of the 2019-20 campaign.
A new boss may be appointed in Glasgow, though, with the Hoops yet to make a decision on their long-term plans.
Neil Lennon was brought back to the club for a second spell as boss when Brendan Rodgers departed for Leicester.
He has helped to get the club over the line in another title triumph and is considered by many to be the ideal candidate to fill a permanent post heading forward.