Following Havertz's international debut on Thursday, Boldt ruled out a move in the foreseeable future in an interview with Sport1:
"There is no reason to be uneasy. 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."
Per Goal's Jamie Smith, Bayern full-back Joshua Kimmich added fuel to the speculation after playing alongside Havertz for Germany, saying the 19-year-old would "suit" the Bundesliga champions.
The Gunners have also been linked with the youngster, per Darren Wells of the Mirror.
Havertz has been one of the top teenage sensations in the Bundesliga after making his debut in October 2016. As well as a full Germany international, he is one of the best passers in the Bundesliga:
Kimmich went out of his way to praise Havertz after Germany's 3-0 win over Russia:
Leverkusen have been committed to building through their academy and clever transfer business, but their results have been poor so far this season. After back-to-back losses before the international break, they sit in 13th place in the Bundesliga, just two points above the relegation spots.
That has led to some speculation their top youngsters could be on the move. Havertz is just one of several highly rated talents, as the side also includes Leon Bailey and Jonathan Tah.
It's the midfield man who is expected to be the hottest commodity, however:
Bayern have had a disappointing start to the season themselves, which could result in a lot of transfer activity around an aging squad.
The Bavarians have a tendency to lock up Germany's top talents. Leon Goretzka, 23, joined the club in the summer from Schalke, and a one-two punch of him and Havertz could set the team's midfield for years to come.