Gallas has been ruled out of the rest of the season after picking up a calf injury in the first leg of Arsenal's Champions League quarter-final with Barcelona.
Before being sidelined, Gallas had formed a key partnership alongside summer signing Thomas Vermaelen at the heart of the Gunners defence.
The Frenchman's stance over a new contract could mean he has played his last game for the club, however.
Gallas, 32, is determined to sign a two-year extension to his current deal, but Gunners boss Arsene Wenger will not shift from his policy of offering one-year deals for players in their thirties.
Keown, who had eight successful years under Wenger at the club, has told Gallas he must acknowledge that he will not be offered a two-year deal - and admits the 32 year old could leave north London this summer.
"He looks like he wants two years but the club don't offer players of his age more than one year. He'll have to come to terms with that," said Keown.
"If he trusts his ability he will play one more year and then look for another year after it, but if he gets a better offer then he may go off to pastures new. That decision rests with the player more than it does the club."
Vermaelen has been a revelation at Arsenal since Wenger plucked the Belgian from Ajax in a £10million transfer last summer.
Wenger is a shrewd mover in the transfer market, and Keown has warned that the 60-year-old will have already begun searching for a long-term replacement for Gallas.
"Wenger will be looking for new talent out there," said the 43-year old.
"Everyone had doubts about Vermaelen but he has been absolutely superb this season. You can be sure that he'll be on the hunt for another one of him in Europe this summer."
Another veteran defender seeking a new contract at the Emirates Stadium is 35-year-old Sol Campbell.
The former England man signed on for a second spell at Arsenal in January after walking out on League Two side Notts County.
Campbell has performed admirably since his return to north London and Keown believes his former team-mate deserves a new contract at the club.
"Sol has done exceptionally well this season," said Keown, who made over 300 appearances for Arsenal between 1993 and 2004.
"I applauded him coming in but whether Wenger keeps him is another matter.
"With a full pre-season training behind him then I think he might be even better for us than he has been this season. That needs to be contemplated."