Sanchez has seen his place at the franchise come under threat since the arrival of Smith, who was chosen by the Jets in the second round of this year's draft.
However, Namath believes that any athlete who needs another person to make them reach their limit should not be in the team, likening the situation to the signing of Tim Tebow last season.
"I mention competition, I'm talking about the opponents. You know, when it comes to their own team, I'm tired of that bringing in competition to make him better. Getting Tebow to make Sanchez better, bringing in so-and-so," said Namath.
"Excuse me, these are professionals. You think they're lying around there? They're supposed to be competing every single play to convince themselves they're doing their best. Some animals need to be pushed. Those kind of guys you got to get rid of. You don't even need them on the team.
"Unfortunately, some of those guys are on various teams. But that's the coach's fault, that's the people who pick the players fault. And if they can't tell those are the kind of guys, well they don't want those kind of guys that need to be pushed. Get rid of them now."
Namath played for the Jets for the majority of his illustrious career and was inducted into the NFL Hall of Fame in 1985.