The Frenchman joined Spurs on a one-year contract in August after failing to agree a new deal at the club's fierce rivals Arsenal.
Gallas has impressed during his time at White Hart Lane and has made 21 appearances for the club in all competitions.
Spurs boss Redknapp has confirmed talks have started over an extension for the 33-year-old and is optimistic Gallas will be part of his plans next season.
"I think it probably will get done," said Redknapp.
"William wants to stay and he has been outstanding."
Meanwhile, Redknapp accepts Spurs are no longer realistically in the Premier League title race, but feels second place is not beyond his team's reach.
He added: "We won't finish above Man United. If I had to pick one team who might have a chance of catching them I would go with Chelsea.
"We have a chance to finish above the others. It's quite open.
"City are a good side, but it's not impossible and it's not impossible to finish above Arsenal. The belief is there."