The report is citing the M.E.N as saying that Real Madrid's Varane and Bayern Munich star Boateng are among an eight-man list of targets being eyed by Mourinho as United look to splash out on a centre-back once again this summer.
Boateng left City for Munich in 2011 but he recently admitted he would consider leaving the club and Karl-Heinz Rummenigge has revealed the German could leave the club.
It was reported ahead of the summer transfer window past year by the Daily Mail that Chelsea were considering making a move to sign Boateng.
Mourinho knows he needs to strengthen his squad if United are to compete for top honours next season having finished a whopping 19 points adrift of Premier League champions Manchester City last season.
He said, "If a club comes to us and he says that he wants to join that club, then we will negotiate".
Boateng admitted last month he is keen on testing himself overseas, having struggled with Manchester City in the Premier League in 2010-11, and the desire for a transfer is still present according to Rummenigge. But the offer has to be important.
The German centre back is now away on worldwide duty, and at this point in time, it seems unlikely that a move would be made for his services before the World Cup is finished.