The Algerian has been in excellent form for the Portuguese side this season.
The Sun claims high-flying Leicester City are also considering a move for the Algerian - who impressed with two goals at the 2014 World Cup - while West Ham failed in a bid to bring him to the Boleyn Ground in the summer.
The Portuguese side - who have previously sold the likes of Cristiano Ronaldo and Nani to United - are said to want £12m for their key man (via The Sun).
Based on his performances so far this season, the fee required to bring Slimani to the Premier League may turn out to be an excellent bargain. His 13 goals in 16 league matches makes him the second highest goalscorer in the Portuguese top flight this term.
And with Louis van Gaal's side often struggling for goals - though they did score three in their last game, against Newcastle - that kind of goalscoring return would improve their chances of securing a top four finish immensely.