Chelsea released a statement after the defender's comments claiming they remain open to retaining him, though it depends on the wishes of a new manager, who will replace current interim boss Guus Hiddink at the end of the season.
Desailly moved to Stamford Bridge in 1998, the season Terry made his debut for the senior squad, and the Frenchman hopes to see his former team-mate find a solution to stay at the club.
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"This is a story that has not finished," Desailly told the Daily Express.
"The club are saying that they are still negotiating.
"I think they will probably renew. There is more talking to be done."
Terry has claimed he will not leave Chelsea for another Premier League club. Major League Soccer and China are thought to be his most likely destinations come July.