He controversially moved on to Chelsea for a (then) club record fee of £2.1million just before the first season of the new Premier League got underway, Norwich turned down the bid, but he forced it through by threatening to go on strike and refuse to play for the club again. At the time the deal was a record sale for Norwich, As part of the deal a clause was included to ruled Fleck out of playing against Norwich the 1st time they met just a couple of weeks later. Despite his now legendary status at Norwich, at the time he was probably one of the most hated players among Norwich fans. The move proved unsuccessful; Fleck scored just four goals in 48 appearances and was loaned out to Bolton Wanderers and Bristol City. He missed out on a place in Chelsea's squad for the 1994 FA Cup Final, which they lost 4–0 to Manchester United.