NEW YORK — The New York Knicks and coach Mike Woodson are completing a multiyear deal that could be announced this week, a person with knowledge of the situation said Tuesday.

Woodson led the Knicks to an 18-6 record and a first-round playoff loss to Miami as interim coach after replacing Mike D’Antoni on March 14. The Knicks’ victory in Game 4 of the series ended an NBA-record, 13-game postseason losing streak that dated to 2001.

Top players Carmelo Anthony, Amare Stoudemire and Tyson Chandler all endorsed Woodson’s return and will get their wish, the person told The Associated Press on condition of anonymity because the contract is not finished yet. The New York Post reported Tuesday that the sides were committed to getting the deal done before the Memorial Day weekend.

Woodson will become a full-time NBA head coach again for the first time since a six-year run in Atlanta ended in 2010. The Hawks improved their win total in each season, finishing 53-29 in 2009-10, but Woodson wasn’t retained after they were swept in the conference semifinals for the second straight year.

He sat out a season before joining D’Antoni’s staff as an assistant last summer. D’Antoni resigned when the Knicks were 18-24 and in danger of missing the playoffs. Woodson won his first five games, quickly getting the Knicks back into the race.

Madison Square Garden chairman James Dolan said in announcing D’Antoni’s departure that the coaching position would be evaluated after the season. Woodson became an obvious choice to return by then, particularly after the Knicks removed the interim tag from general manager Glen Grunwald, his former college teammate at Indiana, late in the regular season.

Woodson, a first-round draft pick of the Knicks in 1980, has a career 224-292 record as an NBA coach. He was an assistant to Larry Brown in Detroit when the Pistons won the 2004 NBA title.