Per ESPN's Adam Schefter, "multiple teams" have called the Jets to ask about Darnold's availability.
Schefter did note the Jets aren't "turning away calls" for Darnold, but they also haven't "made any final and firm quarterback decisions about what direction they want to or are ready to go."
New York currently owns the No. 2 pick in the 2021 NFL draft. This year's class is expected to feature a number of quarterbacks taken in the first round. Clemson star Trevor Lawrence is the presumptive No. 1 pick to the Jacksonville Jaguars.
Ohio State's Justin Fields, North Dakota State's Trey Lance, BYU's Zach Wilson and Alabama's Mac Jones are among the other potential first-round options.
Darnold's future with the Jets has been up in the air since the end of the regular season.
ESPN's Rich Cimini reported last month that new head coach Robert Saleh and offensive coordinator Mike LaFleur "have watched a lot of Sam Darnold tape and they believe he has untapped potential."
Saleh also praised Darnold's "unbelievable talent" during his introductory press conference last month, though he didn't commit to the former USC star as the Jets quarterback next season:
"There's a lot to Sam but there's so many discussions that need to be had and so many moving parts with regard to the rest of the roster, the whole entire building, the draft, free agency all of it to give an answer on where we are at that point, with (general manager) Joe (Douglas) and his staff, there's just a lot of discussions that have to be had."
Darnold is under contract for at least one more season, though the team has until May 4 to decide if it will exercise the fifth-year option on his rookie deal for 2022.
Per Spotrac, Darnold will only count $9.79 million against the salary cap in 2021.
The Jets traded up in the 2018 NFL draft to select Darnold with the No. 3 pick. He's shown flashes of the talent that made him a top prospect, but has struggled to find consistency through his first three seasons.
Darnold has thrown for 8,097 yards, 45 touchdowns and 39 interceptions with a 58.9 completion percentage in 38 starts.