According to the Daily Express, the Barca academy graduate is keen to leave the Nou Camp for first-team football with Arsenal and Liverpool eager to snap up a bargain.
The 23-year-old had been tipped for the top at Barcelona but has struggled to cement his place in the starting lineup and has long been linked with a move to the Premier League.
Speaking to Spanish newspaper El Confidencial, his agent, Juan de Dios Carrasco, confirmed Montoya is exploring his options ahead of the January transfer window.
"It's very difficult but we are speaking to the club about finding a solution in the winter market. Luis Enrique has already told him he is behind Dani Alves and Douglas, but it now seems he is also behind Adriano."
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Barcelona have plenty of competition for places at Montoya's favoured position, right back, which means a move could be on the cards.
Liverpool brought in Javier Manquillo from Atletico Madrid as confidence wavers in Glen Johnson, but the Spaniard has not covered himself in glory so far. Admittedly, the Liverpool defence as a unit has performed poorly this term.
As for Arsenal, the Gunners signed Mathieu Debuchy from Newcastle over the summer but the Frenchman has battled injury in his first few months of the season.
That has forced Calum Chambers to step in but Arsene Wenger views the young England international as a more natural centre-back and could look to bring Montoya in to provide competition for Debuchy as another orthodox full-back.
Loan or permanent?
A loan move has been mooted in the past, but it sounds like Montoya is finally resolved to leaving Barca for good if given the opportunity.
Carrasco continued: "My advice to him is to ask for a transfer, not to go out on loan.
"We are faced with him being loaned out until the end of Luis Enrique's contract in 2016, but Martin neither wants to go on loan or wait to see whether Enrique renews or not."