Havertz, 22, put his slow start to life at Chelsea following his £72million move from Bayer Leverkusen behind him with a fine end to last season, capping it with his side's goal in their Champions League final victory over Manchester City.
Tuchel said: “The guy is so full of talent he will not have a relaxed second with me.
“Because if you have this amount of talent you have to push yourself to the absolute maximum and the absolute maximum for this guy, nobody knows.
“He has the body, he has the talent, he has the head, he has belief to play at the very top, he has everything.
“I found Kai very, very strong when he came back — I was very pleased with his attitude towards training and in the pre-season matches, and very early in the season.
“I found him a little bit tired after the national break, he was also a little bit ill during the matches for Germany, but now he is in very good shape and has had a good impact, a good physical game against Zenit when he came off the bench.
“He is super-important for us."
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