The veteran has a deal to 2024, but is a target for former club Fluminense and Saudi Pro League teams.
Lampard said, "It's an amazing achievement physically. I played until 38, 39 but the last couple of years in MLS I started to understand that my body was telling me 'don't do it anymore'.
"I've got nothing but praise for the career that Thiago has had and to see him at this level, he's an inspiration to the players, who could and should learn a lot from him in terms of how he looks after himself off the pitch and how he approaches training daily and what he demands from his team-mates.
"That's something that has to rub off at this club more at the minute. He's been special.
"He's demanding and that's a good thing. I wouldn't say he's the most vocal, each to their own personality wise. Some players will be really vocal, he's not that but he's one of these players that leads by example.
"Players that play next to him or with him understand what the levels are. If you don't (give) them you'll get a look or a talk or something. He's not a screamer and shouter but he certainly demands from people around him and I think that's a good thing.
"At this level, you need players like that, and they're not everywhere."