Martinez has been linked to several top clubs, including Manchester United and Barcelona, but a return to Arsenal is also a prospect.
The Gunners see Martinez as a potential replacement for David Raya, who may be tempted to leave for Real Madrid or Atletico Madrid.
Raya is being eyed by Real Madrid as a potential replacement for Andriy Lunin.
Martinez, 32, has expressed a desire to return to London Colney, where he would likely be the team's number one goalkeeper.
