Depay was sold to the Ligue 1 side in a £16m deal a year-and-a-half ago - half the amount United, then managed by Louis van Gaal, paid to PSV Eindhoven - after failing to make the grade in his two seasons at Old Trafford.
The 24-year-old has got his career back on track in France, however, and he produced a promising display on his return to Manchester in midweek as Lyon stunned Manchester City at the Etihad Stadium.
Amid talk of a buyback clause being inserted in Depay's contract, Mourinho admitted that he would like to see the 39-cap Netherlands international realise his full potential with the Red Devils.
"He's potentially a very good player," he told reporters. "I think when Mr Van Gaal decided to buy him he did well, he knew him very well from the national team, he was very young when at the World Cup he had flashes of top quality.
"He was playing well in Holland, we know the Dutch league is not the same but he was showing very good things. So I think Mr Van Gaal and Manchester United did very well to buy him.
"He didn't succeed in his 18 months but he's very young so I think it's important for the club to complete control of this talent and we all wish he plays very, very well at Lyon and why not to come back because everyone here likes him."
Depay scored seven goals in 53 appearances for United, compared to 19 goals and 13 assists in his first full Ligue 1 campaign.