The 23-year-old centre-back has emerged as one of the most promising defensive prospects in the game and has reportedly attracted the attention of several clubs.
Manchester City and Chelsea are among those to have been linked with the Argentina international, along with Barcelona and Napoli.
However, he has a long-term deal with Villarreal and club president Fernando Roig says they will only consider letting him go for the right price.
"Musacchio has a contract until 2018, therefore he will be here for four more years," said Roig.
"If someone wants to come and pay what he is worth, then we will talk.
"For the player to leave, it depends on three parties, not just one or two - he has a contract.
"If he is wanted, then for Villarreal it is fine, but only if the money is paid up front."