Mourinho – the self-proclaimed 'Special One' – has tipped his former Chelsea number two to become the first Scotland boss to lead the national team out of a group stage at a major tournament.
Clarke has faith his team can do it too but admits they will have little room for error as they prepare for battle with the Czech Republic, England and Croatia.
"I think Jose is probably looking at the quality of player we've got in the squad," said Clarke.
"It's nice when a top coach – and make no mistake Mourinho is a top coach who played a big part in my development when I worked with Jose – says those kinds of words.
"But he's looking at the all-round strength we have in the squad and the results we've had recently. And yes, there is a good chance we can come out of the group.
"But we have to make sure we get our preparation right and get everything right on the day."
The Scots have their final tune-up session on Sunday as they take on Luxembourg after Wednesday's impressive 2-2 draw with Holland sent belief in the Tartan Army sky high.
It is a different story to when Clarke was appointed two years back. He inherited a side unsure of itself after Alex McLeish's troubled tenure, but bit by bit the Scots have developed a swagger which Clarke hopes can now enable them to stride beyond the groups.
"I've got to be honest I don't like the word arrogance but I know where everyone goes with it – it's a confidence," he explained.
"You have to go into these matches against the top teams with a belief that you can get something out of the game.
"We did that the other night and it's a mindset that we have to take that into the tournament.
"It's three tough games against three difficult opponents – but we have to relish that challenge.
"Experience helps. I've banged on a couple of times since getting this job about international experience. Being used to playing international matches and being successful.
"Not losing is important and the recent run we've been on is decent. We want to continue that into the tournament.
"I haven't so much had to drill it into them about self-belief but I have my own way of working.
"I've never approached a football match as a player, coach or a manager thinking, 'We're going to get beat today'.
"I've never thought that once in my career. Maybe subconsciously I've managed to put that point across to the players.
"We have to respect every team we play, no matter how big or small they are.
"But it's about reaching our level of performance. If we can reach our level of performance I believe we can get results against most teams."