But Garrard hadn't played in a regular-season game in the NFL since 2010 because of injuries.
The 35-year-old Garrard was signed in March to provide veteran competition for Mark Sanchez.
Despite not playing for the Jets, Garrard could still potentially be around the team this summer.
Garrard was also asked if the team drafting Smith played any role in his decision.
That doesn't faze Garrard, who made a Pro Bowl in nine seasons with Jacksonville.
"If I have to get a first down, I can, " Garrard said with a laugh.
Ryan didn't want to comment on Garrard, saying he would wait until the QB's retirement becomes official.
Idzik said Smith will compete with Sanchez, McElroy, David Garrard and Matt Simms for the starting job this season.
"My knee is great now and I've moved on from that, " Garrard said.
Garrard, who signed Monday with the Jets, dealt with back and knee injuries that sidelined him the last few seasons.
Create London's Hadrian Garrard said it would be a "counterpart to the big, flashy, flag-waving expensive ticket offers that we've seen previously".
"Nothing's changed, " Sanchez said of his approach without Garrard on the team.
They signed David Garrard, who hasn't played in the NFL since 2010.
Garrard was expected to be in the mix to compete for the Jets' starting job along with Sanchez and second-round pick Geno Smith.
Garrard said he would consider that, as well as finishing his degree and pursuing a radio or TV gig as a football analyst.
"Honestly, they just told me that I have a chance to compete for the starting job, " Garrard said during a conference call Tuesday.
The team's quarterback position certainly is more crowded than ever, with the Jets bringing in Garrard to compete with Sanchez for the starting job.
Garrard said he would feel "comfortable" in a West Coast-style offense that new offensive coordinator Marty Mornhinweg is expected to run with the Jets.
The Jets already have Sanchez, Tim Tebow, Greg McElroy and Matt Simms under contract, and have expressed interest in David Garrard and possibly Brady Quinn.
There is one less competitor in the mix, however, with David Garrard planning to retire because his balky left knee has continued to give him trouble.
So with Garrard stepping away and New York cutting Tim Tebow two weeks ago, Sanchez, Geno Smith, Greg McElroy and Matt Simms are left on the roster.
Graff says he's not interested in selling out, even at a time when private equity firms like Ronald Burkle's Yucaipa are investing in British jewelers Garrard and Stephen Webster.
"It would be an enormous gesture to name a Latin American pope, " said Virginia Garrard-Burnett, a professor of history and religious studies at the University of Texas at Austin.
The Jets had signed Garrard with the intention of having him compete for the team's starting quarterback job, even though he had not appeared in an NFL game since 2010.
Tebow is part of a crowded quarterback depth chart that includes Sanchez, David Garrard, Greg McElroy and Matt Simms, and it's believed the Jets still are trying to trade him.
Goodson's arrest came just two days after quarterback David Garrard, another recent free-agent acquisition by the Jets, said he planned to retire from the NFL because of a chronic knee injury.
"It would be an enormous gesture to name a Latin American pope, " Virginia Garrard-Burnett, a professor of history and religious studies at the University of Texas at Austin, said earlier this week.
CNN: First Latin American pope 'very exciting,' faithful say
Garrard told SiriusXM NFL Radio on Thursday that his surgically repaired left knee kept swelling up on him after workouts, and that forced him to walk away from the game and consider retirement.
Garrard was in training camp with Miami last summer and appeared to have a chance at the starting job, but a knee issue that was covered on HBO's "Hard Knocks" ended those hopes.
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