The 21-year-old has scored more goals for England (three) than Manchester United (two) this term after a below-par start to the season for Jose Mourinhos side.
Mourinho has defended his use of Rashford but the forward has started just twice in his favoured central striker role this season despite the struggles of first choice Romelu Lukaku.
Rashford missed a golden chance as he emerged from the bench in Uniteds shock 2-1 win against Juventus earlier this month and the Times claim the Serie A giants are interested in signing the striker.
Juventus are said to have compiled a dossier on Rashford and have made background checks on his character and mentality.
Rashfords current deal runs until 2020 though United have the option of extending that by a further 12 months.
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The Manchester-born forward adores the club and the Red Devils would be loathed to lose one of their academy products.
However, Juventus poached Paul Pogba from Old Trafford in 2012 and the prospect of playing alongside Cristiano Ronaldo is understandably tempting.