The Italian champions are said to be well aware that Rashford is far from a regular starter for the Reds and sense an opportunity to take him to Turin during the summer transfer window.
The 21-year-old was a substitute during United's recent Champions League win in Turin and has struggled to make himself a regular fixture in Jose Mourinho's first team.
Reports in Italy are claiming that Juve are putting together a 'dossier' on the player's background and character to see if he would be able to fit in at their club.
Rashford is under contract with United until 2020 and although he would be reluctant to leave his boyhood club, he is also said to want assurances over whether he will be able to develop with the club.
As well as Rashford, reports are also claiming that Juve are keeping tabs on David De Gea's situation and could attempt a double raid on Old Trafford.
The goalkeeper's future is far from certain at United, with the Reds said to be keeping tabs on Everton's Jordan Pickford, should he leave.