Reports claim the 22-year-old is out of contract at the end of the season, but he has put off talks over a renewal as he looks to concentrate on breaking into the Barcelona first-team.
Arsenal and Liverpool are both reportedly primed to offer him a contract in January in the hope that he'll agree to a free transfer switch instead.
The La Masia product has a tough fight on his hands to displace current first-choice right-back Dani Alves from Gerardo Martino's starting lineup.
Arsenal boss Arsene Wenger is eager to strengthen his defensive options, and with the future of Bacary Sagna currently uncertain, the report suggests Montoya is under consideration as a possible replacement.
But the Arsenal target has been tracked by Liverpool manager Brendan Rodgers for the past 12 months, and he is lining up a contract offer of his own.
Other European clubs monitoring Montoya include Inter Milan, with new owner Erick Thohir keen to hand Walter Mazzarri the required funds to help Inter qualify for next year's Champions League.
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