The Spaniard has been one of the Reds’ top targets over the course of the last few transfer windows, with his contractual situation with the Catalan giants unclear.
Montoya’s current deal expires at the end of the season, which has led to talk that he may leave for free in search of regular action.
However, talks between the club and the player are ongoing, and it is understood that the 22-year-old is ready to commit himself to the La Liga champions.
The defender is thought to have concerns about his role at Barca, with Dani Alves’ presence having limited him to just 14 starts all season.
But, Montoya sees himself as a successor to the Brazilian, and may be ready to bide his time in his quest to be the club’s number one right-back.
Liverpool are ready to offer him the role he desires, but it is thought that he is not ready to leave.
Roma are also keen, and both sides may look to snap him up on a pre-contract agreement if he fails to reach a deal with Barca.