Carter ranks fourth in the all-time NFL marks for receptions (1,101) and receiving touchdowns (130), while his tally of 13,899 receiving yards is the ninth-highest in the league's history.
Marshall currently has 712 receptions for 9,050 yards and 57 touchdowns to his name, and the 30-year-old is keen to play on for the foreseeable future in order to improve those figures.
"They're going to have to rip the jersey off of my back [for me to stop playing]. I've always said I want to play 14 years. That's always been my goal. But maybe [I'll play until I'm] 36 years old. Who knows?" Marshall told ESPN.
"I'm trying to pass Cris Carter in everything. I don't think I have it in me to go for Jerry [Rice]. That's 20 years I would have to play.
"Maybe with modern medicine and all this new technology, I could potentially play that long, but I've had three hip surgeries. I'm just asking for six more [years in the league]."
Marshall recently signed a three-year contract extension with the Bears that will keep him in Chicago until the end of the 2017 season.