The Japan international impressed during his two Champions League group stage outings against Liverpool, and has a release clause of just £7.25million.
Jürgen Klopp is driving the pursuit of the 24-year-old who scored at Anfield in October during the Reds' thrilling 4-3 win.
Minamino, who has scored nine times in 22 appearances this term also caught the eye on Tuesday night with another glimmering performance as the Reds booked their place in the last 16 with a 2-0 victory.
The ECHO understands Man United are one of a number of clubs reportedly interested in acquiring the versatile winger along with some Bundesliga and Serie A sides.