Redknapp wrote for 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 £8.5million.
"I watched him play for Peterborough last season — ironically at Palace — and all my scouting reports about him were great.
"My chief scout Ian Broomfield’s reports were all glowing. We were looking at him but then, suddenly, the price shot up and QPR got relegated.
"But he’s a pint-sized frontman, a great mover and a terrific finisher. He scored 13 goals last season for a team struggling against relegation from the Championship.
"Gayle has made his way up through non-league and made his mark at Dagenham and Redbridge, having been taken there by one of the great football finders in John Still, the club’s former boss.
"Now Eagles chief Ian Holloway has taken a punt and given him his chance in the top flight for next season, so good for him.
"He could fall flat on his face of course but I don’t think that’s going to happen somehow."