Bloomberg's Devin Banerjee and Kiel Porter report that Winkelried could become co-CEO of TPG, along with co-founder Jim Coulter.
Winkelried was one of the most senior executives at Goldman Sachs during the financial crisis, and was touted as a possible replacement for chief executive Lloyd Blankfein.
He stepped down from his role as co-president and co-COO at the US investment bank in 2009.
He was later referred to as "The man who walked away from Goldman Sachs" in a 2010 Fortune article by William D. Cohan.
He has kept a relatively low profile since then. He signed on as an adviser to TPG's credit funds in 2011, and earlier this year invested in Orchard Platform, a technology and infrastructure provider for marketplace lenders.
He reportedly entered into talks about the co-CEO role in June.
TPG manages $74 billion in private equity holdings, credit assets, real estate, and hedge funds, according to Bloomberg.
We've reached out to TPG for comment and will update when we hear back.