The Jets are looking to add another offensive skill position piece to the puzzle, but general manager John Idzik may first have to fend off a pair of division rivals.

The Daily News has learned that the Jets, Patriots, Dolphins and Steelers are in the hunt to land veteran running back Maurice Jones-Drew. The teams are expected to meet with the Jones-Drew camp at league meetings this week.

The News reported two weeks ago that the Jets had serious interest in the former Jaguars running back. Jones-Drew, 29, visited the Steelers last week, but left without signing a contract.

A CBS Sports report last week indicated that Jones-Drew, who has spent eight seasons in Jacksonville, was looking for $3.5 million per year in a new deal, but two sources said that number is high. The Dolphins brought in Broncos free-agent running back Knowshon Moreno for a visit last week, but he left without a deal.

Two different sources told the News that Idzik’s hard-line stance cost the Jets an opportunity to sign their top running back target early in free agency. That player signed with another AFC team.

Jones-Drew, who has rushed for 8,071 career yards, would be a good find for Idzik & Co. on the secondary free agent market.

The Jets are looking for a running back to complement Chris Ivory, who has had durability concerns throughout his career. Jones-Drew, who has had six seasons with at least 40 receptions, would also provide a pass-catching dimension that fits in Marty Mornhinweg’s offense.

The three-time Pro Bowler averaged a career-low 3.4 yards per carry last season, but he could provide another quality option with a shared workload for an offense that had a dearth of weapons last season. Jones-Drew had 1,117 total yards and five touchdowns last season.

The Jets, who have about $30 million in salary cap space, have been hunting for bargains since signing wide receiver Eric Decker to a 5-year, $35-million deal at the start of free agency. They inked four-time Pro Bowl QB Michael Vick to a one-year, $5 million deal last week.