The former Brazil goalkeeper, 32, spent the second half of last season on loan at Hoffenheim in the Bundesliga.
Gomes has not appeared for Spurs since a Europa League tie against PAOK Salonika in November 2011.
"My situation at Tottenham is not good," Gomes told The Sun.
"I can leave on a free, even though I have a year left on my contract. I have told them I want to go."
Gomes cost Spurs £7.8million when Juande Ramos signed him from PSV Eindhoven in June 2008.
A return to the Dutch Eredivisie outfit would suit him, and he added: "I would love to rejoin PSV. It would feel great to return as I spent wonderful years with them.
"I feel fitter than ever. I'm in my early 30s and I can still perform. If PSV want me, I would say yes."
PSV's current shot-stoppers are Poland international Przemyslaw Tyton and Netherlands Under 21 keeper Jeroen Zoet.