England midfielder Lampard was given a new one-year deal at Stamford Bridge after a season which saw him overtake Bobby Tambling as the club's 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 last season and was not a firm fixture in interim boss Rafael Benitez's defence even when fit.
But Lampard told the Sun: "I know JT will want to stay, he's said he'd love to stay at Chelsea. He feels the same as me.
"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 are veterans of three Premier League titles, Champions League and Europa League wins and multiple FA Cups and League Cups with the club and Lampard believes having an established spine to the team has been vital to the club's 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."