England international Lampard, 34, signed a new one-year deal last week, following a season that saw him overtake Bobby Tambling's record as the club's leading all-time goalscorer.
The future of club captain Terry, 32, has been the subject of speculation after an injury-hit campaign during which he was often left out of the side by interim boss Rafa Benitez.
The defender has one year left on his existing deal at Stamford Bridge.
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."
Terry made 27 appearances for Chelsea in all competitions last season, scoring six goals.