The Blues exited the Champions League on Wednesday night after a 4-2 aggregate defeat by Ligue 1 side Paris Saint-Germain in west London.
If they’re not in the Champions League, they won’t attract the best players in the world
Chelsea appear unlikely to qualify for next season’s competition as the Blues are in tenth place in the Premier League table and 10 points behind fourth-placed Manchester City.
Italy manager Antonio Conte, who previously managed Juventus, is the favourite to replace interim head coach Guus Hiddink at the defending Premier League champions.
Former Manchester United midfielder Keane assessed the challenges that Conte – or any other potential successor – will face at Stamford Bridge next season.
“It is a great opportunity for whoever comes in here,” Keane told ITV Sport.
”There is quality at the football club. There is talk of Terry leaving. Does Hazard leave? Is it a rebuilding job? It may be a bit strong of a word but it is a big job.”
Keane added: “If they’re not in the Champions League, they won’t attract the best players in the world. That will make it hard for the manager.”
Chelsea make the trip to Everton in the FA Cup fifth round at Goodison Park on Saturday afternoon.
Hiddink is unbeaten in domestic competitions with Chelsea after he replaced Jose Mourinho at the west London side in December.
Get 8/1 enhanced odds on Tottenham to win or 11/1 enhanced odds on Liverpool to win at White Hart Lane on Saturday afternoon. Click here to sign up now. T&Cs apply.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news