The Swede had previously been released from the club after sustaining a cruciate knee ligament injury during the Europa League quarter-final.
The Red Devils often struggled to find a way past teams last term, when Zlatan Ibrahimovic provided the key impetus with 17 Premier League goals, although no other player was able to reach double figures.
But Mourinho, speaking ahead of the clash with West Ham United, made it clear that Lindelof would be an importantly versatile asset at Old Trafford this season.
The United boss said: "He's injured, and needs time to recover". It's not something that's urgent, it's not desperate to have it done or not.
"He wants more at football's highest level, so we are having conversations and we are discussing the possibility of him staying with us for the second part of the season".
Ibrahimovic recorded a goal every 137 minutes in his debut season for United last season.
"Victor can play right-back and can play centre midfield, we got a centre midfielder and we got an attacking player", he said.
His American doctors are amazed by his progress, but have advised him to strike a balance between rest and rehabilitation.
Zlatan Ibrahimovic has once again taken to social media to prove that he is 100% not human as he steps up his recovery from the ACL injury that brought a premature end to his 2016/17 season. "I don't think I am in a position of moaning, crying, contesting or saying I am not happy". "I'm happy with the effort the club did and I'm happy they managed to do 75 percent of the work before the Premier League starts".
"I hope he doesn't leave Madrid". I will go with what I have to try to win everything. We also got a central midfielder and a striker.