According to Italian news outlet Calciomercato.com, the 23-year-old has been identified as a possible low-cost option to arrive in January for the Nerazzurri, as they continue to consider their options in midfield.
While the former Elche midfielder featured regularly for Roma last season, this season he has struggled to make his way in the team, only managing to play in the UEFA Europa Conference League under new manager Mourinho.
He is reportedly not in Mourinho's plans at Roma, and if they are looking to sell him, Inter would be very interested in a player of his profile.
Inter are currently looking at their options in central midfield, especially with Marcelo Brozovic's contract expiring next summer, with his future still uncertain as renewal talks continue to stall.
Signing Villar would fit Inter's midfield very well, with him having the qualities that Inter are looking for to potentially replace Brozovic.
As reported earlier by Yoonis Mohamed (via The Goalpost), Mourinho is looking to make plenty of wholesale changes to Roma's squad, particularly after the horrible 6-1 defeat against Bodo/Glimt in the Europa Conference League last week.
Villar is one of those names earmarked for a move, with Mourinho wanting to stamp his authority on the squad, making it his own after inheriting the squad from Paulo Fonseca.