QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
Ilkay Gundogan has commited his future to Borussia Dortmund by signing a new contract.
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.