Brendan Smith, the former Red Wings defenseman who came to the Rangers at the trade deadline, is reportedly staying in New York.

Smith, 28, who would have been an unrestricted free agent on Saturday, agreed to a four-year extension worth a reported $17.4 million, according to TSN and TVA Sports in Canada. The Rangers said there would be no announcement yesterday, indicating that a deal has yet to be finalized. Smith’s agent, Anton Thun, did not return a phone call.

The 6-2, 211-pound right-hander, a physical player with an edge, played parts of six seasons with Detroit and appeared in 18 games with the Blueshirts last season, as well as all 12 playoff games, often paired with Brady Skjei.

Smith can play the left or right side, and has averaged between 18 and 19 minutes per game. In 309 regular season games, he has 16 goals and 71 points and 310 penalty minutes.

“It’s been a blast,” Smith said on break-up day after the Rangers lost to Ottawa in the second round of the playoffs, and indicated a desire to return. “It’s arguably the best team I’ve been on. I really enjoyed being here.” The two sides have been talking regularly since.

If the numbers and term are accurate, Smith’s annual salary cap charge would be $4.35 million. Smith earned $3.25 million last under his old contract, with a $2.75 million cap hit.

The deal would leave the Rangers with approximately $15.6 million in cap space.

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The Rangers are still working to sign two restricted free agents, center Mika Zibanejad and right wing Jesper Fast, general manager Jeff Gorton said Sunday in Chicago. They also are in the hunt for a center, another defenseman and a backup goaltender. Those needs could be addressed as soon as Saturday, when the free agent market opens.