Musacchio's agent, Marcelo Lombilla, has warned David Moyes his client won't come cheap amid interest from a number of clubs.
The Argentine defender has also been linked with Liverpool and Fiorentina, and the 23-year-old is under contract until the summer of 2018.
As a result, the likes of Liverpool and United would be expected to hand over at least £16.5m to land the talented centre-back.
"The player's contract expires in 2018 and his market value is approximately £16.5m," he is quoted as saying in Marca. "He is a very young player. For now it will be difficult to transfer him.
"The player would be interested in projects like Fiorentina, but we are waiting for concrete proposals in the future. We do not have any kind of scheduled meeting with their officials.
"In June we will see. He is very attached to [former Villarreal players] Gonzalo Rodriguez and Borja Valero and often maintains contact. The club Fiorentina is growing. I think my client would be fine with a coach like Vincenzo Montella."
With Nemanja Vidic and Rio Ferdinand approaching the latter stages of their Old Trafford careers, Moyes is thought to be on the lookout for defensive reinforcements for United.
Musacchio has impressed for Villarreal since joining from River Plate in 2009, and he has two caps for his national team.
Liverpool were linked with the defender, but after spending big money on Mamadou Sakho and Tiago Ilori, not the mention the free agent acquisition of Kolo Toure, the Anfield club may feel they're well stocked in that department.