Rice has a connection in the Jets organization with general manager John Idzik, who spent six years in Seattle as the vice president of football operations before taking the GM job with the Jets in January of 2013.
Rice was released by the Seahawks on Feb. 28 for salary-cap reasons. He would have counted $7.3 million against the cap. He missed the second half of the 2013 season after tearing an ACL in a game at St. Louis, but was given clearance by his doctor to begin running and cutting drills on Monday.
Seahawks coach Pete Carroll has said they were interested in bringing Rice back, but the price may become too high if the Jets have a serious interest in him.
Rice, 27, caught 15 passes and scored three touchdowns before his injury last season. He caught 50 passes for 748 yard and seven touchdowns in 2012.