The eccentric Brazilian has even lost his place on the bench in recent weeks with Carlo Cudicini preferred as back-up to summer arrival Friedel.
Gomes will be given the opportunity to prove a point to his manager when he starts the Europa League Group A clash with PAOK Salonika, with Redknapp making a host of changes.
And the Spurs boss believes the shot-stopper, who was signed for £7.8million from PSV Eindhoven in the summer of 2008, still has a role to play at White Hart Lane, despite being linked with a return to his former club.
Redknapp said: "I think he does have a future with Tottenham.
"He's obviously upset he's been left out. It's been difficult. I brought Brad in, there's competition for places and I just decided to go with Brad. It was my gut feeling."
Redknapp will make 10 changes to his side on Thursday from the one that beat Wolves 2-0 on Saturday.
With one eye on Sunday's league game against Liverpool, the 64-year-old has left Luka Modric, Scott Parker, Gareth Bale and Emmanuel Adebayor at home.
That means youngsters Yago Falque, Jake Livermore, Andros Townsend and Tom Carroll are likely to be given a chance to impress in what is expected to be a white-hot atmosphere generated by PAOK's fanatical support.
"It's not a case of prioritising a game, it's just (using) what I have got," Redknapp said.
"I couldn't bring players out here, play them on Thursday night and play the same group against Liverpool.
"If I get a few injuries I have no back up. I have nine senior, very, very good players who are injured.
"Some of them have played two international games so I wanted to change the team around. I have done that. I have not been able to use the strong group I have for this first game because they're not fit."