Lampard ended speculation about his future by signing a new one-year deal to stay at Chelsea after a season which saw him overtake Bobby Tambling as the club's all-time record goalscorer.
The future of club captain Terry, two years Lampard's junior at 32, has also been the subject of discussion after he struggled with injuries this season and was not a firm fixture in interim boss Rafael Benitez's defence even when fit.
Terry's existing deal is due to expire at the end of next season.
"I know JT will want to stay, he's said he'd love to stay at Chelsea. He feels the same as me," Lampard told The Sun.
"Why play anywhere else when you love the club you're at? JT's the captain of the club and does a brilliant job.
"At the start of next season, I think that's when the club will take a view on it. I know what my view would be."
Both players have won multiple trophies with the club, including this month's Europa League, and Lampard believes having an established spine to the team has been vital to their success.
However, he laughs off the suggestion that the senior players in the dressing room are able to influence owner Roman Abramovich's hiring and firing of managers.
"One thing that has helped us remain successful over such a long period is a strong core, strong spine," he said. "I mean that in terms of players - their ability, personality and the leaders.
"You need people like that in the dressing room. But the idea of the dressing room being too strong? Certainly not.
"I've never heard of any players here being able to ask our owner to sack a manager or even discuss anything to do with the structure of the club. If you wanted to take that chance you would probably get sacked yourself."
Frank Lampard urges Chelsea to extend John Terry stay
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