According to a recent report from El Nacional in Spain, the Dutch attacker has failed to satisfy new manager Xavi thus far.
With the attacker's contract set to expire in 2023, there are rising indications that the next couple of transfer windows may be Barcelona's best chance of making a significant profit.
The Catalan club is thought to be interested in selling and would accept a bid of around £33 million.
Looking to bolster his attacking ranks, the Portuguese strategist, who has previous experience coaching the Dutchman from their time together at Manchester United, may want to reunite with his former players.
Although much has been made of Depay's capacity to produce at the greatest level, Mourinho, who spoke highly of the Holland international earlier this summer, does not share those fears.
“He is a really good professional. People can look at him and probably think he’s a party boy,” Mourinho told talkSPORT. “I think he got this maturity in Lyon which is sometimes what players need.
“Sometimes they can go too early to the biggest clubs where they are not ready to cope with it. Where they are not ready to understand that in the biggest clubs there is internal competition, that you can not play all the time. That there are fantastic players to fight with you for a position. They can lose a little sense of reality and become a bit childish. Which is what happened.
“So when he decided to go to Lyon it was a great move for him and now he goes to Barcelona with maturity, with a good football age and I believe the Barcelona culture of football will help him also to level up in this important part of his career. But good memories of him and I repeat – he was a good professional.”