The Gunners are pushing hardest for the Argentina defender, having launched a third offer with Ajax on Wednesday.
The latest bid is worth £35m plus £5m in add-ons.
Speaking to De Telegraaf, Dutch journalist Marcel van der Kraan said that Martinez is hoping for a move to Manchester United instead of the North London club.
"Martinez will also have his hopes pinned on United, who are an absolute top club for him.
"Ajax will really cash out for Martinez and go to £38.7m-£43m (€45m-€50m), but that is the advantage if two clubs bid, then it suddenly goes higher."