That's according to Obama administration officials. They say Indyk will return to his previous job at The Brookings Institution think tank.
An announcement is expected later today. The officials spoke on condition of anonymity because they were not authorised to discuss the matter publicly. The State Department declined to comment.
Indyk is a former US ambassador to Israel. He was appointed to the envoy post last July when Secretary of State John Kerry announced peace talks would resume with the goal of reaching a settlement within nine months.
The peace process is now in hiatus. It's not immediately clear if Indyk will be replaced. His deputy is Frank Lowenstein. He will assume the envoy position on an interim basis, the officials said.