Paris Saint-Germain are also thought to be in the frame, despite reports suggesting no official contact has been made between the club and his representatives.
With a return to the Premier League on the cards, it is thought Mourinho is already working on plans to revitalise the club.
Rashford has shone for United ever since he burst onto the scene against FC Midtjylland in the Europa League in February.
Seven goals in 13 appearances for the Red Devils has been a proof in point.
Rashford played 64 minutes of United’s 2-0 win over Crystal Palace last night before he was replaced by Memphis Depay.
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