The 31-year-old made history last weekend with a goal against Reading that took him level with Sir Bobby Charlton’s 43-year goalscoring record of 249 goals.
Rooney, speaking after the 4-0 win over Jaap Stam’s side, described reaching the record as a “proud moment.”
The 53-year-old, when asked whether Rooney could remain producing at the highest level, said: “I don’t know, it depends on him — especially on his brain, on his desire.
“I think everything is about desire, more important than anything else. I think he has motivation so if he keeps motivation he can play.
“I don’t even know his current deal. I am not worried with my players’ contracts. I leave this to [executive vice-chairman] Mr Woodward to deal with.
“In spite of not working with him [before this season], I had always a good relation with him. I always had a good feeling with him — a good professional, a team player. I saw him always sacrificing for the team.
“He played against me when I was in Real Madrid in Madrid. He played almost left-back. I always saw him sacrifice for the team and, with me, he is the same.
“He is on the bench, he comes in. He plays, he doesn’t play. But he is always positive with the group, a good captain, so I am really happy.
“He is what I always felt. A humble guy, a good guy — a professional, team guy.”
The Mourinho era has overseen an important transitional period for the captain. He has, almost since day one, been a central figure at Old Trafford, always existing at the heart of proceedings with virtually no interruptions.
But following 14 straight years of playing no less than 42 games a season, with various international tournaments to contend with on the side, Rooney’s legs have called time on playing regularly at the highest level, and Mourinho has realised this.
His new role revolves less around on-pitch exploits; United fans no longer expect the Englishman to produce powerful performances every week. Appearances will be more sporadic as the months go by, and his influence will be felt more in the dressing room and at Carrington.