The Red Devils have had to deal with a shaky defence all season, and according to the Mirror, Solskjaer believes Varane is the man who can help tighten the screws alongside captain Harry Maguire.
The 28-year-old has one year left on his contract with Los Blancos and United believe they can secure his signature for around £40m. He has spent a decade with the LaLiga giants, making 359 appearances in all competitions, and winning 18 trophies during that time.
United had previously tried to bring Varane to Old Trafford but failed to get a deal over the line; however, Solskjaer is quietly optimistic of finally bringing his man to Manchester this summer. The United boss has admitted his side need two or three world-class signings this summer to challenge for the title, with a central defender a priority.
"Harry has been amazing since he came to the club,” said Solskjaer. “He's been more or less ever-present, so of course, when a player is a leader, a captain, the status of him, his presence is missed.
"But then we have players who can come in and it's a chance for everyone to take on that little bit of leadership. We need to do that when he's gone. You can hear him in the stands when he's not playing. He's important for us and someone else has to take that responsibility now, because I'm sure that in the next two games we'll be without him. Hopefully, we can get him back for the final, but who knows? I don't know yet."