Mourinho is now a free agent after being sacked by AS Roma this week.
"I remember interviewing Mr Mourinho when he was at Madrid or Chelsea when he came over to Los Angeles," Leboeuf said on ESPN.
"He admitted that the last thing he would love to do in his coaching career would be to get the Portuguese national team job. I think that's going to be his goal.
"It's tricky right now with Roberto [Martinez] but I really think he can be patient and see how it goes during the Euros and then maybe jump into the seat if he has the chance to."