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."
- Sports & Recreation
- Bobby Tambling
- Rafael Benitez