Arsene Wenger has earmarked Gallas as one of three potential successors to former skipper Thierry Henry this season, along with Gilberto Silva and Kolo Toure.
"I am 30 years old and I want to have more responsibilities both for my club and for the national team," he told L'Equipe.
"I am attracted to the idea of giving advice to the youngsters, to leading a group.
"If they chose me to become the captain, I would not say no.
"On the contrary, it would make me very proud to wear the captain's armband for Arsenal."