The Jets have contacted Owens' agent, Drew Rosenhaus, and have debated the idea of bringing the high-profile wide receiver to training camp.
A deal between the Jets and Owens still is considered a long shot; one person estimated the Jets' chances at signing Owens at "20 percent."
Another NFL source told ESPN.com's Tim Graham that the Jets' interest in Owens was "very minimal."
Ultimately, this is similar to the situation in which the Jets contacted quarterback JaMarcus Russell but never signed him.
Still, the Jets are debating Owens' acquisition, as coach Rex Ryan wants any player who improves the team's chances of winning.
The Cincinnati Bengals remain the favorite to sign Owens.
The Bengals are offering an incentive-laden contract, and they have told Owens, 36, he has until Wednesday to agree to a deal.
Even so, now that the Jets have made contact with Owens, the receiver has options in the days ahead.
Adam Schefter is ESPN's NFL Insider. ESPN.com's Tim Graham contributed to this report.