Jack Mills, the agent for quarterback for Baker Mayfield, says New England indicated interest in trading up to the second pick to draft the QB. (0:50)

Baker Mayfield's agent says the New England Patriots indicated to him they were considering trading up to the No. 2 overall pick in the NFL draft if the Heisman Trophy-winning quarterback out of Oklahoma was available.

Mayfield's agent, Jack Mills, made his comments on "The Business of Sports with Andrew Brandt" podcast.

Mayfield ended up being picked No. 1 overall by the Cleveland Browns, but Mills said the Patriots were interested enough in his client to swing a blockbuster trade if Mayfield fell one spot. Mills said the Browns kept their interest in Mayfield quiet right up to the draft and that the New York Jets indicated that they planned to pick him if he was available at No. 3.

"When he visited the Jets, they pretty much said you're our guy if you're there," Mills said.

Asked if on the day of the draft whether he was expecting the Jets to select Mayfield, Mills said: "We knew that was the bottom line.

"We had another team which is going to surprise you. Another team had said, 'You may get a big surprise on draft day, at No. 2, if he's available.' And it was the Patriots," Mills said. "They had 23 and they had 31 and they had two seconds. We thought, 'That's gonna be a heck of a move, to get up that high from where they are.' And of course he wasn't available so we never knew if that was a reality or not."

After selecting running back Saquon Barkley at No. 2, New York Giants general manager Dave Gettleman said he had no interest in trading out of the pick. However, he said Monday on WFAN's "The Afternoon Drive with Carlin, Maggie & Bart" that he did receive "one very reasonable offer" for the pick but wouldn't go into details.

The Jets selected quarterback Sam Darnold at No. 3 overall with Mayfield off the board.

The Patriots, who traded backup quarterback Jimmy Garoppolo to the San Francisco 49ers last season, had been thought to be in the market to draft Tom Brady's eventual successor this year but waited until the seventh round before picking a quarterback, selecting Danny Etling.

Brady, who will be 41 when the 2018 season starts, confirmed Monday that he will play this season and reiterated that he hopes to play into his mid-40s.