Marshall was injured during last Sunday's 27-22 loss to the Los Angeles Chargers when he landed awkwardly out of bounds while attempting to make a catch.
"I'm a competitor, and I don't want to go out like that," Marshall told ESPN this weekend. "I'm definitely not going out like that."
Marshall, who will be 34 years old in March, said he is focused on getting healthy and wants to play a 13th NFL season.
"That's my mindset right now," said Marshall, who signed a two-year contract with the Giants in the offseason.
Marshall had 18 catches for 154 yards and no touchdowns in five games this season.
Marshall is one of three Giants wide receivers -- along with Odell Beckham Jr. and Dwayne Harris -- to suffer season-ending injuries last week.