The Spanish goalkeeper, who turns 38 this month, spent the second half of the season on loan at Aston Villa.
And the idea of returning to the Milan bench as a backup for Gianluigi Donnarumma does not appeal to him.
Reina has decided to leave Milan, who will let him go on a free transfer if he finds a club.
Valencia are showing interest and have already been in contact with the player’s agent.
Reina may also have the option to stay in Italy, with a number of Serie A sides asking to be kept informed.
At the moment there are no advanced talks for Reina, who has a net salary of €3m-per-season.