Reports suggest that Ian Holloway's side are close to agreeing a deal in the region of £8.5m for the 22-year-old with the Posh.
Redknapp wrote in hos column in The Sun: "Premier League new-boys Crystal Palace are taking a gamble on 22-year-old Dwight Gayle but it's a risk worth taking.
"He's a young lad, a striker and the deal I'm told could end up rising to around £8.5m. I watched him play for Peterborough last season — ironically at Palace — and all my scouting reports about him were great."
Gayle scored 13 goals in the Championship last season for Darren Ferguson's side.