Terry's current deal expires at the end of the season and the Blues defender claimed last week that the club had not offered him an extension.
Lampard, who enjoyed a successful season with Manchester City after being released by Chelsea, encouraged his former club to reconsider their position towards former teammate Terry.
Read more: Terry to leave Chelsea after contract snub
Terry told The Times: "Some players pass through clubs, even top players, but some players are the club.
"These are the ones you have to keep, especially when they remain a big part of your first XI. I still feel John is the best defender at the club.
"He's Mr Chelsea. He loves the club. He's one of the greatest players the club has ever had.
Current Chelsea interim boss Guus Hiddink has suggested Terry may yet be offered a new contract once next season's manager is named.
Lampard said he would expect any new boss to want to keep Terry at Stamford Bridge.
"They're going to get a top manager and I wouldn't be surprised if that manager wants to keep John Terry around," said the club's all-time leading scorer. "I hope so anyway."