General manager Joe Douglas told reporters Wednesday he "will answer the call" if teams want to discuss the 23-year-old.
Even though the team will listen to offers, Douglas noted the organization still values Darnold highly.
"Our stance on Sam hasn't changed. He's an extremely talented player. Very smart, very tough. We have no doubt he's going to achieve his outstanding potential," he said.
Douglas has been coy about what the Jets plan to do at quarterback under new head coach Robert Saleh.
Here's what Douglas told reporters Jan. 5, nine days before Saleh and the team agreed to a contract:
"I think that Sam's going to be a great quarterback. I'm excited to get a head coach in here, go through our process. Had a great conversation with Sam yesterday. I won't go into the specifics, but I think Sam has a very bright future in this league. So we're going to get a head coach in here, we're going to get together and we're going to talk about quite a few decisions."
The Jets are in an ideal spot given their draft position and cap situation. They own the No. 2 pick, giving them the option to select a top quarterback even if Trevor Lawrence goes to the Jacksonville Jaguars.
Many projections have linked New York to BYU star Zach Wilson. There are also some established NFL quarterbacks who could be available in free agency or via trade, including Dak Prescott and Deshaun Watson.
Per Over the Cap, the Jets have the second-most cap space in the league this offseason with $67.9 million. They also have an extra first-round pick (No. 23) from the Jamal Adams trade with the Seattle Seahawks.
Darnold is entering the final guaranteed season of his rookie contract, and he has a fifth-year option available that must be picked up by early May. The USC product has thrown for 8,097 yards and 45 touchdowns with 39 interceptions and a 59.8 completion percentage in 38 starts over three seasons.