Gomes has fallen well down the pecking order in the last two years following the arrivals of Brad Friedel and Hugo Lloris. His last appearance for the London club came in November 2011 and he has rarely made the bench in the last 18 months.
The Brazilian was keen to secure a move back to his homeland in order to try to win back his place in the national squad ahead of the 2014 World Cup, but he now looks set to join Hoffenheim, who are in talks with Spurs over a possible six-month loan deal for the 31-year-old.
Gomes is one of a number of squad players that Spurs boss Andre Villas-Boas is looking to move on before tonight's 11pm deadline.
David Bentley and Jermaine Jenas look set to move to QPR, while Tottenham have also given permission for Fulham to talk to midfielder Tom Huddlestone.
Andros Townsend may also leave on loan, with QPR also thought to be one of a number of interested parties in the young winger.
Villas-Boas played down talk of a last-ditch attempt to bring in a marquee signing yesterday following the club's 1-1 draw at Norwich.
The Portuguese has been heavily linked with a move for Internacional striker Leandro Damiao and other hitmen such as Lyon's Lisandro Lopez and his team-mate Bafetimbi Gomis.
Gomes later confirmed that he was en route to Germany to have a medical with the Bundesliga club.
He tweeted: "On my way to Germany for a medical !!!!
"Thanks all for the support , love you ! When you are in a difficult moment a simple word can make the difference!"