The 22-year-old is out of contract in the summer and is free to discuss terms with foreign outfits, including Liverpool.
Brendan Rodgers is reportedly keen to add the right-back to the Anfield ranks as he looks to compensate for the frequently injured Glen Johnson.
Managing director Ian Ayre has been sent to the Nou Camp last year to declare Liverpool's interest in bring Montoya to Merseyside when his contract expires.
However, Montoya is keen to remain at the club and compete for a first team place with the La Liga giants.
So far Montoya has made 14 starts for Barcelona in all competitions but still sits behind Dani Alves in Gerardo Martino's pecking order.
AS Roma are also believed to be monitoring the situation and were reported to have made contact with the player last week in a bid to secure his services.