Liverpool signed the Spain midfielder on Friday, paying an initial fee of just £20million to lure him away from Bayern with a further £5m in add-ons.
The deal was done in time to enable the 29-year-old to make a shock debut for Liverpool against Chelsea this weekend.
The Blues know first-hand how devastating Thiago can be, with the Spaniard playing a key role in Bayern's Champions League last-16 aggregate victory over them last season, and Lampard has hailed him as one of the best midfielders in the world right now.
“Thiago is an incredible player,” said Lampard, speaking hours before Thiago’s move to Liverpool was announced on Friday.
“As you say we saw him first-hand - quality on the pitch, personality on the pitch and off the pitch.
“The quotes from Hansi Flick this week have been talking about him on both fronts and when you hear that from their manager, who has just such success with him at the centre of the team, I think it speaks for itself.
“He is an absolute world-class midfielder in the modern day. If he does come to the Premier League it will be a big plus and a big plus for the team that he comes to.”