Jennifer Lopez has her sights set on her new home in the wake of her split from Ben Affleck ... it's a famous piece of L.A. real estate, but it's not going to be a simple purchase.

Sources with direct knowledge tell TMZ ... J Lo is in negotiations to buy the Azria Estate in Holmby Hills, and she's close to striking a deal.

The 30,000-square-foot estate is listed for $55 million ... but our sources say Jennifer is trying to negotiate the price down to somewhere in the range of $30 million to $39 million.

Late BCBG owner Max Azria used to live here -- hence the name -- and the estate has 14 bedrooms and sits on a 3-acre lot with gardens, a greenhouse, a guest house and an infinity pool with a sauna ... plus an in-home theater and game room.

However, there's a catch here ... the Azria Estate was put up for auction earlier this year and billionaire investor Ron Burkle placed the winning bid at $30 million. He's reportedly now locked in a lawsuit against Max Azria's widow, Lubov Azria, over an alleged breach of contract.

The legal dispute's been playing out since May ... and our sources say J Lo started showing renewed interest in the home in August, and in the last few weeks she's taken several tours of the place.

We're told J Lo is negotiating with both Burke and Lubov to potentially strike a deal here.

J Lo has a couple connections to the Azria Estate ... it served as a filming location in her movie "Atlas" and she took a gander at it back in March 2023, when she and Ben were looking for a home together.

What's more, the estate shares a property line with Diddy's house, which just went on the market for $61 million ... and famous neighbors include Tom Ford, Sean Parker and Jimmy Iovine.