Falcao is set to leave United after a disappointing season under Louis Van Gaal, scoring just four Premier League goals in 21 appearances, and will return to parent club AS Monaco at the end of the season.
He has been linked with a move back to former club FC Porto but Liverpool are keeping tabs on the Colombian striker and could make a move to keep him in the Premier League.
Brendan Rodgers is on the look out for another striker as he has suffered the same problem with his summer signing, Mario Balotelli, who has struggled to impress and could be on the move again after one season.
Balotelli has just a single Premier League goal in 14 appearances and his performances have come under heavy criticism.Embed from Getty Images
Falcao could potentially be another problem for Rodgers to deal with but Liverpool could be in luck if there is any revival of his past form.
Falcao has scored an impressive 195 goals in 317 club appearances, but at nearly £40 million, it could be risky business for the Merseyside club.
Would a move for Falcao be a huge risk for Brendan Rodgers and Liverpool?