Sky News reported that Sun Capital Partners are close to sealing a £400 million deal with an official announcement due shortly.
Following the merger of Keepmoat and rival Apollo in 2012, the firm employs more than 3,200 full-time staff across 22 regional offices.
The company is one of a string of house builders, which ended up in the control of Lloyds Banking Group, after it bought the assets of rival HBOS.
Any deal would see Sun and TDR seeing off competition from rival bidders including Apollo Management.