The Knicks are on the verge of landing Grant Hill, according to two NBA sources.

Hill, the Suns free agent, deliberated for the past few days between making the jump to New York or staying with the Phoenix Suns, who are in rebuilding mode.

Hill is close to accepting the big challenge of the Big Apple.

“It’s not 100 percent done, but he’s leaning,’’ one source said.

The third time appears to be the charm. The Knicks failed to woo Hill when he became the NBA’s most-sought-after free agent in 2000 and were rejected again two years ago when he decided to remain in Phoenix.

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Hill and his wife, Tamia, a recording artist, are enamored with New York but were concerned about uprooting their two children in grade school. Hill, who dealt with major injuries earlier in his career, also was worried about leaving the renowned Suns’ training staff.

But Hill is about to choose the Knicks, who could be one of the heavyweights in the Eastern Conference. Hill would be slotted in as the starting shooting guard, supplanting Landry Fields and giving the club more leadership, shooting, defense and the depth the team lost in last season’s Carmelo Anthony trade.

Hill, at 39 is the second-oldest player in the league, averaged 13.2 points per game last season on 48.4 percent shooting in 30 minutes a night. The ankle and foot problems from earlier in his career have not plagued him since coming to the Valley of the Sun. He has missed three games combined in the past three seasons.

Hill played his first season in Phoenix under the coaching staff of Mike D’Antoni, Dan D’Antoni and Phil Weber.

“If it wasn’t for his relationship with Mike and the staff, this wouldn’t even be a consideration,’’ one source close to Hill said yesterday.

With Hill, the Knicks starting lineup would be Hill, Anthony, Chauncey Billups, Amar’e Stoudemire and perhaps Jared Jeffries at center.

Contracts can’t officially be signed until tomorrow, when training camp begins. From a basketball and career standpoint, a move to the Knicks was a no-brainer. But a person close to Hill said his family life is equally important.

The Suns have made a strong push to keep Hill, even with rebuilding plans, regarding him as their glue.

“Grant is an absolute first order of business and top priority,” Suns president Lon Babby said of Hill one week ago when team executives were allowed to start talking to players after the lockout. “I can’t contemplate him not being here. He represents everything we want the franchise to stand for — on and off the court. He’s our ballast.”

The Knicks still have moves to make beyond Hill. Small forward Shawne Williams, a revelation last season, wants to come back and he would solidify the bench. It is unclear if the Knicks would still have room to sign center Jeff Foster or Kurt Thomas.

Jeffries agreed to terms Tuesday and could share the starting role with Ronny Turiaf. The Knicks are also interested in adding 7-2 French prospect Alexis Ajinca of Toronto, who would fit well in D’Antoni’s system.