The 22-year-old faces an uncertain future at the Nou Camp, as he is out of contract in the summer and yet to agree on a new deal.
Inter Milan are also said to be monitoring the right back, but their Serie A rivals Napoli have shown the strongest interest thus far.
Former Liverpool and Chelsea boss Rafael Benitez has already added three Spaniards since joining Napoli, in the form of Pepe Reina, Raul Albiol and Jose Callejon. He is now hoping to make Montoya the fourth, despite the interest from two of the Premier League big guns.
Benitez is set to do battle with both his former club and the Gunners, and will be hoping the Spanish connections in Naples will play their part.
Arsenal are set to have money to spend in January as Wenger looks to add players to create a serious title challenge.
The league leaders are looking for an extra defender and a striker in January, whilst Brendan Rodgers is keen to add another attacking full back to his set up at Anfield, after changing to a system which deploys wing backs in recent weeks.
Montoya is free to sign a pre contract agreement with another club in January if he has not yet signed a new deal, or leave for a small fee.