Sterling is expected to tell Liverpool boss Brendan Rodgers that he does not want to sign a new deal at Anfield when contract talks resume this week.
The 20-year-old has two years left on his current deal and reports suggest he has already turned down an improved contract offer worth ??100,000 a week.
However, World Cup winner Desailly says there is enough money in the game and thinks that Sterling could be motivated to move clubs to win the Premier League title which eluded Liverpool legend Gerrard.
He said: ???He must have his own reason. As for money, in football there is money because we are dealing with talent, you cannot quantify, it will never stop, it will always go higher and higher.
???You see the TV rights that we have now for the Premier League and for the players it will follow up, the sponsorship is coming in. He must have a personal reason to have the desire to go higher. Everyone is playing for their own situation.
???He feels that to grow he needs to go to a different club. He feels that where he is, even if it is at big Liverpool, he???ll end up being like Gerrard after 10 years not winning the Premier League, then it is his own feeling. We should find out what the main reason was for him.???
Former Chelsea captain Desailly also believes it is time for Petr Cech to leave Stamford Bridge unless he wants to spend the majority of next season on the bench.
He said: ???It is obvious ??? he needs to leave. He has only two more years left of playing football, he needs to go and enjoy it if he is someone who is motivated to play, unless he wants to sit and play 10 games in the year and grab his money.???
Desailly also claimed that Blues fans will probably have to get used to the sight of Cech turning out for one of the club???s Premier League rivals with the goalkeeper being linked with moves to both Arsenal and Manchester United.
He added: ???You have to accept that idea. In the course of the season it is not good but from the beginning of the season you have to accept that he will face Chelsea in the future.
???He???s not scoring goals and he???s not a striker – he???s a goalkeeper. You have to allow the room of risk for Petr Cech because he has given quite a lot for Chelsea and it is time to go now.???