Both Arsenal and Manchester United want to sign Martinez this summer, but neither club have yet to reach an agreement on a fee with Ajax.
Martinez is waiting for an agreement to be in place before he decides where he wants to go, but it has been suggested that Manchester United have the edge due to Erik ten Hag.
However, the Argentine centre-back is also intrigued by the prospect of playing for Arteta and believes just like Manchester United, the Gunners would also suit his playing style.
He told Ajax in a meeting earlier this week that he wants to move to the Premier League.
Martinez interrupted his holiday to deliver the message to Ajax and wants the club to agree to sell him.
The onus is now on Arsenal and Manchester United to find an agreement with Ajax.
Martinez is currently back in Argentina for the second part of his holiday after spending time on Ibiza.