The 22-year-old is out of contract at the Nou Camp next summer, which means Wenger could sign a pre-contract agreement with him in January with a view to a free transfer in the summer.
Or the Gunners boss could look to agree a cut-price move for the defender with Barcelona in the January transfer window, allowing the Spanish youth international to join Arsenal in January.
Tottenham did similar with Lewis Holtby when they brought the Germany international to the Premier League from Schalke.
Montoya, a right-back, could potentially provide cover for Bacary Sagna, who is yet to agree a new Arsenal contract and could leave the club for free at the end of the season.
Montoya is highly-rated in Spain, and has made 22 appearances for the under-21 side – he’s won the European under-21 tournament with his country twice, both in 2011 and this year in Israel.
But with Dani Alves ahead of him in the pecking order at Barcelona, the Spaniard may decide his best chance of first-team football lies elsewhere.
Arsenal like to make use of free transfers, having signed both Yaya Sanogo and Mathieu Flamini for nothing this summer.