Gomes has found himself well down the pecking order at White Hart Lane this season and has yet to feature for Andre Villas-Boas' side.
The Brazilian is keen to move on in this month's transfer window and Spurs are unlikely to stand in his way if they receive a suitable offer, according to Sky Sports.
The news has alerted a number of clubs across Europe to Gomes' possible availability either on loan or in a permanent deal.
Italian giants AC Milan are thought to be interested in signing Gomes as they look to bring a new goalkeeper to the San Siro.
A couple of unnamed Dutch clubs are also believed to be monitoring Gomes' situation, with the 31-year-old enjoying a successful spell in Holland with PSV Eindhoven prior to his move to Tottenham.