Richardson said Wednesday he received a call from the Jets soon after arriving in New York for pre-draft festivities.
"They wanted to know my information as far as whether that's the right number to reach me in case something does happen, with them trading up," he said Wednesday at an NFL community event in Manhattan.
It's common for a team to call potential picks a few days before the draft, but it's unusual to contact a player seemingly out of reach.
The Jets, picking 16th in the first round, are exploring the possibility of moving up for Richardson, according to league sources. But it's a long shot, considering they'd probably have to jump 11 or 12 spots.
The Jets have greater needs than running back, but Richardson is the No. 1 player on their draftboard, ESPN's Sal Paolantonio reported.
Richardson said he'd like to play for the Jets, who hired a run-oriented offensive coordinator -- Tony Sparano -- and plan to get back to the Ground-and-Pound mentality that led them to back-to-back AFC Championship Games in 2009 and 2010.
"I would love it," Richardson said. "I don't feel bad about playing for any team. Football is football, and it's the National Football League."
General manager Mike Tannenbaum, who traded up in the first round in 2007, 2008 and 2009, said he's open to moving up and down in Round 1. To get up to the fourth or fifth spot, it would take a substantial package that probably would include next year's first-round pick.
In 2009, the Jets jumped from 17 to five, taking quarterback Mark Sanchez. But they received a sweetheart deal from the Browns and former Jets coach Eric Mangini, who received the Jets' second-round pick and three players -- Kenyon Coleman, Abram Elam and Brett Ratliff.
This time, it would take a lot more to make the jump, but the Jets are known to covet Richardson.
"I do think Trent Richardson is a great player," Tannenbaum said last week. "I think he will help a team. He's a three-down back, he can pass protect and he can catch the ball. He played for coach (Nick) Saban and, obviously, had a lot of success. ... There are a lot of things to like about Trent. So whoever gets Trent will have a really good back for a long, long time."
The Jets have Shonn Greene, who rushed for 1,054 yards in his first season as the feature back, but they have depth issues. LaDainian Tomlinson, a free agent, won't be back. That leaves Joe McKnight and untested Bilal Powell as the backups.
Sparano would like to use a two-back system. He also has new backup quarterback Tim Tebow, who will be deployed in the Wildcat and perhaps as a fullback and H-back.
"That's a great comparison," he said. "I look at his game and I try to revolve my game around his game. ... That comparison, yes, I do love that comparison. It puts a smile on my face every time I hear that."