Bayern have been linked with the 19-year-old as they aim to add midfield depth, with experienced options like Arjen Robben and Franck Ribery heading towards the end of their careers.
And Havertz's Germany team-mate Joshua Kimmich added to the speculation by saying: "I cannot buy him, but Kai Havertz is a player who would suit us well."
Havertz has started all 11 games for Leverkusen in the Bundesliga this season, scoring three goals with his side in the bottom half of the table.
13 - Kai #Havertz has assisted 13 goals in his career in the #Bundesliga at the age of 18 years and 307 days, more than any other player at this age since detailed data collection 2004-05. Creative. @bayer04_en @DFB_Team_EN pic.twitter.com/HKgaU58zSL— OptaFranz (@OptaFranz) August 29, 2018
And Boldt feels Havertz will be staying with the club for the foreseeable future despite Bayern being linked with a move for the teenager.
"There is no reason to be uneasy," he told Sport1. "His future lies in Leverkusen, where Kai has an environment where he can excellently develop.
"It's nice to see the boy progressing from month to month, and of course we're pleased that he has done so well on his [full] national debut, confirming our path in Leverkusen.
"Club, player and everyone has agreed that Leverkusen is the right club, so logically there were no requests."