Seemingly every AFC East team has expressed interest in signing free-agent running back Dalvin Cook this summer, and it appears the New England Patriots are attempting to step up their pursuit of the veteran.

While Cook is reportedly slated to visit with the New York Jets this week, the Patriots have been in contact with the former Minnesota Viking about setting up a potential visit, according to ESPN's Jeremy Fowler.

However, Patriots head coach Bill Belichick would not confirm nor deny the report while speaking with reporters Thursday.

"Yeah, no, I'm not going to talk about players that are not on our team," Belichick said, via Doug Kyed of the Boston Herald. "It's a long-standing policy that I'll continue to stick with."

Patriots director of player personnel Matt Groh was asked Wednesday about the possibility of adding Cook this summer. He replied, per Kyed:

"We talked to DeAndre Hopkins, that's well known. We explore as many options as we can. Dalvin's another player, this is a really, really unique situation with both of these players. You don't typically have players of this caliber available at this time. The contracts that are signed for players right now are nowhere near in the neighborhood of the contracts that these players are generally expecting to sign.

"Usually, these are all minimum guys with splits. So this is a unique situation and any unique situation, I think everybody evaluates and looks at, you know, with Dalvin. And we saw firsthand last year going off to Minnesota on Thanksgiving. It was great to spend Thanksgiving in Minnesota. We saw firsthand what he can do."

After failing to re-sign Damien Harris in free agency, the Patriots could use some depth at running back entering the 2023 season.

Rhamondre Stevenson, a 2021 fourth-round pick, is slated to be New England's starting running back this year after rushing for 1,000-plus yards in 2022, which was just his second season in the NFL.

The depth behind Stevenson is questionable with Pierre Strong Jr., Ty Montgomery, Kevin Harris and J.J. Taylor the only other running backs on the roster.

Cook, a four-time Pro Bowler, would instantly become New England's top running back. The 27-year-old has posted four straight seasons of 1,000-plus rushing yards and is coming off a 2022 campaign in which he rushed for 1,173 yards and eight touchdowns in 17 games.

The Patriots have about $15.5 million in cap space, per OverTheCap, which should be more than enough to sign Cook should he be interested in suiting up for Belichick's squad.

If New England strikes out on Cook, there are several other free agents the team could pursue.

The Pats reportedly hosted Leonard Fournette and Darrell Henderson on visits last week, and the likes of Ezekiel Elliott and Kareem Hunt also remain on the market.