Bayern Munich, Liverpool, Barcelona and Juventus are among the clubs to have been linked with a move for Germany international Havertz, who Leverkusen have made clear they will be unwilling to sell for anything less than €100million.
Havertz has now played a part in nine goals (six scored, three assisted) over his past six Bundesliga appearances.
Asked about the talk surrounding his situation after the match, Havertz told Sky: "I do not like to say, of course, that there is a lot of speculation.
"I'm concentrating on this season and will see what happens afterwards.
"I am very grateful to Leverkusen and I don't want to mess it up in any way."
He added: "We're happy about the win. We put it on ourselves to win here and we did that.
"We had to really give everything today and I think we deserved to win in the end."
Bosz felt Havertz showed signs of improvement from Leverkusen's first game back after two months off during the coronavirus suspension.
However, the Dutchman was at pains to point out the victory over Gladbach was the result of a team effort.
"Kai played a little better than against [Werder] Bremen. But it's not about Kai," said Bosz.
"We at Bayer did a great job and Kai was one of them. There were 13 others who played as well as Kai."