"I'd run the risk of it carrying on into next season, and we don't want to do that.
"I'm now just looking to recover from the injury, work really hard and be ready for next season."
Left-back Gibbs played seven times for Arsenal this campaign prior to the depressed open fracture injury suffered in the European game at the Emirates on 23 November.
Gibbs had been suggested as a potential member of Fabio Capello's England squad for the World Cup in South Africa this summer, but the timescale of his recovery rules him out of the tournament, which begins on 11 June.
Arsenal have cover at left-back with French youngster Armand Traore backing up first-choice Gael Clichy.
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