Terry, 35, announced on Sunday his career-long association with Chelsea would end when his contract expires in June.
The defender said it was a "no at the minute" to an extension, but he would not be retiring at the club with who he has won four Premier League titles.
In a statement, Chelsea said they would continue discussing Terry's future – with a stay still an option.
"John requested a meeting with the club the week before last," a club spokesman told The Telegraph.
"In that meeting he asked about the possibility of an extension to his existing contract.
"John was advised that while no new deal was currently on the table, that situation could change in the coming months.
"The club has the utmost respect for John and everything he has helped us achieve to date. He is a fantastic servant of Chelsea Football Club and a superb captain and, as such, the club will keep the channels of dialogue open."
Along with his four league titles, Terry has five FA Cup winners' medals, three League Cup triumphs and a successful campaign apiece in the Champions League and Europa League.