Havertz, 21, has been a revelation in the Bundesliga ever since making his breakthrough as a 17-year-old in the 2016-2017 campaign.
The midfielder, who has been played in an increasingly attacking role over the past two years, has scored 29 Bundesliga goals since the start of the 2018-2019 campaign, while his haul of 12 this term came alongside six assists.
Widespread speculation suggests it is unlikely he will remain with Leverkusen, which failed to qualify for the UEFA Champions League, next term, while Chelsea is said to have positioned itself as the frontrunner for his signature.
Leverkusen is reported to be demanding at least €78 million ($128.1 million)) for the Germany international, whose national team colleague Timo Werner has already made the switch to Stamford Bridge.
But Rolfes, a former Leverkusen midfielder who is now in charge of sporting decisions at the club, insists no club has made an offer for Havertz yet.
"So far we have no offer," Rolfes said. "We know about the interest of clubs, but there is no official offer.
"We have said several times that we will end the season with our entire squad, and that includes Kai. That goes without saying for us."
Although the Bundesliga season is over, with Leverkusen finishing fifth, Die Werkself are still in the UEFA Europa League.
It is due to face Rangers at home next Thursday in the second leg of their Round of 16 tie, having won 3-1 in Scotland five months ago, prior to the coronavirus pandemic bringing a temporary halt to European football.
Should it get past Rangers, Leverkusen will face either Inter Milan or Getafe in the quarter-finals.
At this point the competition will become a mini-tournament made up of single-legged ties, rather than the usual two-legged contests, after UEFA moved the latter stages to neutral venues in Germany because of the coronavirus pandemic.