The Jets are looking for an experienced quarterback to mentor and compete with Geno Smith, and they have an interest in Vick because offensive coordinator Marty Mornhinweg spent four seasons as his coordinator with the Philadelphia Eagles.
The meeting was first reported by NJ.com.
The Jets are battling a deadline because Sanchez is due a $2 million roster bonus on March 25. If they sign Vick over the weekend, they almost certainly would release Sanchez, who has a $13.1 million cap charge.
If the Jets fail to land Vick, they'd be in a tough situation. They could ask Sanchez to take a significant pay cut, although the feeling around the league is that they'd simply release the former starter.
Vick hasn't generated much interest on the open market even though he's considered by many the top free-agent quarterback. He has been linked to the Oakland Raiders and Buffalo Bills, but the Jets will be his first visit.
Vick, who turns 34 in June, played only seven games last season. He was injured and lost his job to Nick Foles. The Jets were impressed by how Vick handled the situation, and they believe he would be a nice complement to Smith, who endured an inconsistent rookie season.
Smith helped the Jets to an 8-8 record, showing promise over the final four games, but the organization has yet to anoint him as the permanent starter.