The Jerome S. Coles Sports Center will be hosting the women’s NCAA Division III tournament this weekend in what may be the last basketball games NYU’s venerable facility sees for a while. There are plans for the historic building to be redeveloped into a multi-use facility and the Violets’ teams to find temporary new homes.

NYU (21-4) will host Virginia Wesleyan (19-9) at 7 p.m. Friday, and Eastern (22-5) will face Amherst (22-3) at 5 p.m. The winners will clash Saturday at 5 p.m. Then comes NCAA fencing on Sunday, and a spring semester of athletics before the building undergoes a huge redevelopment and most sports teams are displaced.

“The new building will be built on the site, and the cool thing is we’ll get a brand-new state-of-the-art athletic facility, as well as a base for the performing arts, a freshman residence hall, residence for faculty, classrooms, a new state of the art sports and recreational facility,’’ NYU athletic director Chris Bledsoe told The Post.

“It’s going to happen we think real soon, whether at the end of summer 2015 or shortly thereafter, so each game that we play — and we’re heading into the end of basketball season — could very well be the last game we play.’’

There have been many games there since the Coles Center opened in 1981, including NCAA regional championships in wrestling, fencing and volleyball, men’s and women’s NCAA Division III tournament games, most memorably the NYU women hosting and winning the 1997 championship.

“The neat thing is we got to host and for the ladies to win the championship on this court is pretty cool. There are lots of memories here,’’ Bledsoe said. “We’ve got a very tight alumni group. They’re often back over the past year — volleyball, basketball, wrestling, fencing — and when they leave, they’re taking pictures, which is poignant. They’re not sure they’re going to be back.

“But the neat thing is we’re replacing it with something cutting edge. … The good news is we’ve got this great new facility to take us into next 30 years of NYU. The bad news is we’re not Giants Stadium where you build the new place, cut the ribbon, play the first game and demo the old one next door. In lower Manhattan, that doesn’t happen. We’re looking at a five-year construction timeline.’’

Bledsoe said NYU is in talks with three other Manhattan colleges to host games and practices, with “98 percent” of basketball and volleyball games being at a single site until the 900,000 square foot facility— which is yet to be named — opens.

It’s part of NYU’s expansion plan in Greenwich Village called NYU2031, an ambitious plan that originally would have encompassed 2.4 million square feet and taken two decades but was approved 44-1 by the city council at a downsized 1.9 million square feet.

It was approved by the council, but apparently not by all neighbors, with groups filing two lawsuits in 2012 to block the expansion.

A judge dismissed the first complaint outright. In the other, while a judge ruled that some city-owned strips were “implied parkland,” in her opinion the strip in front of Coles didn’t fit the category and excluded it from her findings. NYU appealed, and the appellate court unanimously ruled in favor of the school and city, with the case headed for the Court of Appeals in Albany.