The Blues' midfielder believes the skipper will remain at the club, despite the defender's fitness having come into question following limited appearances under Rafa Benitez
Lampard himself only recently signed a one-year contract extension to remain at Stamford Bridge, where he helped the team win a Champions League, four FA Cups and three Premier League titles.
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.''
The 35-year-old also laughed off reports which suggest that the players have influence over the 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.''