The 23-year-old scored 12 times for the Bluebirds last season, 11 of which came in the final 17 matches of the Championship campaign.
Zohore, a Denmark Under-21 international, only signed a contract extension until 2020 in April, but Sky Sports News claims that Hull are eager to get their hands on the forward.
When previously asked about interest in Zohore, Cardiff manager Neil Warnock said: "If I'm to have any chance next season, he won't be going anywhere.
"You can never say never - if someone came in with £20m you can't say no, I'd even sell Sol Bamba for that who has been just as important."
Hull have funds available following the sale of Harry Maguire to Leicester City for £17m as well as the parachute payments they received after being relegated from the Premier League.