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Chelsea have already signed Hakim Ziyech and Havertz's international team-mate Timo Werner this summer, and the addition of the 21-year-old would only add to what has been a big-spending window at Stamford Bridge following last summer's transfer ban.
Havertz had also been linked with the likes of Bayern Munich in recent weeks, butUli Hoeness has confirmed that the Bundesliga champions have pulled out of the race to sign the Leverkusenstar.
Regardless, the German club has insisted that there are no plans to sell Havertz in the short term as the team remains focused on their Europa League campaign with the midfielder fully involved.
Ahead of the continuation of that campaignagainst Rangers on Thursday, Bosz insisted that Havertz is notfeeling the pressure that comes with being linked to a big-money move.
"We are watching all this closely," Bosz told DAZN and Goal."Of 20 interview requests 18 want to speak with Kai. Then we must make sure he doesn't go 18 times.
"He is an exceptional player, but even exceptional players can have a bad day. If we lose, he is always the first to be criticized, even if he didn't play that badly.
"I often talk to him and explain how I saw his game. Then there are games like the one against Hertha Berlin, when the fans whistled at his substitution. I told him that maybe he learned the most in that game, where he was really not good.
"But Kai is an intelligent boy overall and knows how the world works."
Havertz joined Bayer Leverkusen as a youth player in 2010, making his first-team debut in 2016.
The midfielder has gone on to make 148 appearances for the club, scoring 45 goals in all competitions with 37 of those goals coming over the last two seasons.