Dasovic did his B licence course at Largs along with the Real Madrid boss 11 years ago.
He told the Scottish Sun: "We had to be split into four groups and Mourinho - whom I didn't know - was in mine. I think he was second assistant at the time at Barcelona.
"I always hung out with the foreign guys at these things because I could speak a few languages.
"So I was with Jose a lot that week. He was a class guy.
"Back then he was not a big name and was learning his trade at Barca, first under Bobby Robson and then Louis van Gaal.
"But he was just one of the guys and I vividly remember doing karaoke with him on a night out. It was a little La Bamba routine.
"A story that summed him up, though, was how he helped this one guy who was struggling with his on-field drills.
"Jose actually stayed up till 3am with him, talking the lad through it all.
"Jose did not have to do that but he wanted to help the guy out.
"That just shows how humble and down-to-earth he was. I know now he comes over as a bit arrogant but I think you have to do that as a coach to succeed at the highest level."