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Real Madrid and Bayern Munich have both been credited with an interest in the 26-year-old, who has scored 71 goals in 104 appearances for Liverpool since arriving from Roma in 2017.
Salah was on the scoresheet as Jurgen Klopps side beat Tottenham Hotspur in the Champions League final on Saturday night, but the Egyptian refused to commit his future to the Reds after the match.
However, according to AS, United are also considering a spectacular bid for the former Chelsea forward ahead of the 2019-20 campaign.
Salah, who has a contract at Anfield until June 2023, scored 27 goals and registered 13 assists in 52 appearances for Liverpool last season.