Silva, 36, joined Chelsea on a free transfer after leaving PSG at the end of the 2019/20 season, and has already made a big difference at Stamford Bridge.
The Brazil international has helped Chelsea rack up five consecutive clean sheets for the first time since October 2010, with new goalkeeper Edouard Mendy pulling off six shut-outs in succession himself.
Silva won seven Ligue 1 titles and many more trophies at PSG, as well as collecting plenty of individual prizes along the way.
Lampard believes Silva’s professionalism can help a relatively young squad full of new signings gel, and sees few Premier League defenders past or present who can match his achievements.
“In terms of the career he’s had, of course he’s in that bracket, he absolutely walks into that bracket of top centre-backs that includes those players like Van Dijk and Kompany,” the Chelsea boss said.
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“The teams who have achieved in the recent modern day have individuals or pairings that set those kinds of standards, it’s imperative, and we know the importance of defending well to try to win trophies, particularly Premier League titles.
“But they do also need support behind them, around them, in front of them.
“When you look at the performances of Thiago in his early games, the impact I keep talking about him having, he can be a big deal for us.
“But we need a lot more than that, of course, we need a lot more, so I don’t want to crown him with anything now.
“Thiago’s influence has been huge; even without the language his professionalism has been very clear, that rubs off on players, they respect him.
“His performances have been very, very good. He manages himself, he trains well, he prepares well, it’s very obvious from him and understandable why he’s had the amazing career he’s had so far.
“And it’s been great to have him as part of the squad.
“I think players look up to him in how he goes about his daily business and how he performs.
“It’s great for younger players, every player in the squad.
“It’s certainly a pleasure to coach and manage a player with that much intensity in wanting to perform at the highest level.
“Even his age doesn’t feel a big deal. We’re managing him slightly, but when you look at his performances and how he trains, it’s just been a real positive story so far.
“Long may it continue not just for him but for the influence he has on the team.”
Additional reporting by PA.