The 21-year-old looked short of sharpness in Monday’s 3-1 win away to Brighton & Hove Albion but he had trained just four times with his new team-mates and is still working on his fitness.
In particular Lampard has been impressed by the humility shown by the Germany international since arriving.
“I know the player he is from watching a lot of him before he arrived at the club,” Lamaprd said.
“I’ve seen it in training. I think it’s important to be clear that before the Brighton game Kai Havertz had trained for four or five days and two or three of those were a build up to a game so you can’t work that hard.
“Fitness levels for Kai were difficult. They are only going to get better and get better quickly. I’ve seen lots of his talent and have no doubt the impact he will have as a Chelsea player.”
Lampard also provided some detail on his communication with Havertz during the mildly protracted negotiations with Leverkusen, who rejected an initial bid and held firm in terms of their asking price.
Unsurprisingly, Havertz’s friendship with Timo Werner was a factor with the lines of dicussion made trickier due to coronavirus travel restrictions.
“I’m not sure how much you can meet the player in the modern day anyway,” Lampard added. “But I was able to have some conversations with Kai, after the buying process happened, or whatever you want to call it.
“I did as much watching of him as a player as I could, and by that time Timo had arrived at the club, and Timo and Kai are pretty close so I could obviously ask Timo a lot about him, them playing in the national team together. So we had very good background on him.
“But again I was very struck in those conversations with him about his humility, and how he is as a person which I love. I love humility in players who come with the idea they just want to improve and become a success.
“And I know he has great talent. I’ve seen that in the first week that he’s been here.”