Former United winger Jesper Blomqvist believes the club have targeted Sweden's version of Rio Ferdinand in Victor Lindelof.
They had initially been reluctant to sell the centre-back after qualifying for the knock-out stages of the Champions League.
It appears, however, a deal could be reached and Blomqvist has backed his old club's attempts to secure the 22-year-old.
He told the Manchester Evening News: "I was watching the November match between Sweden and France on TV and caught a glimpse of Jose Mourinho in the stand.
"My first thought was that it could only be Victor Lindelof he was looking at. My second thought was what a great signing that would be for the player and Manchester United. It would be perfect.
United in talks for Lindelof
Manchester United have held initial discussions with Benfica over a £38m move for Victor Lindelof
"I have seen him play for the national under-21s, the senior side and in the Champions League for Benfica and he has the right qualities.
"He's quick, confident with the ball, likes to play and is very strong. For United fans I think the best comparisons would be with Rio Ferdinand and Ronny Johnsen.
"I'm not saying he is at their level yet but he is very capable of getting there. He's a mature player and a mature person."
Lindelof has been in Portugal since he was 17 and made his breakthrough last season, establishing himself as a regular in Benfica's team.
Sky Sports News HQ reported last month he was United's top target going into the winter transfer window.
Eric Bailly is injured and will be at the Africa Cup of Nations in January with Ivory Coast, while Chris Smalling and Phil Jones are only recently back from injuries.
Blomqvist has been impressed by Lindelof's development and added: "One thing I like is he hasn't gone an easy route with his career.
"I think making the decision to go to Portugal at that age and making a success of it and then doing what he did for the under-21s shows the character of the player.
"That tells you everything you need to know about him. Obviously, a move to Manchester United is a different level again.
"Not every Swede is Zlatan Ibrahimovic! But you get the feeling that Victor would handle it okay. I don't think Mourinho is actually looking for someone to help them through a crisis.
"He wouldn't be going to England as a saviour for the defence. As much as I think he is a mature lad and can handle pressure I think that could only be a bonus for him."