Sheffield Wednesday are also thought to be interested, as the race to sign the 23-year-old heats up.
The striker clearly attracted the interest of a host of clubs after he scored 12 goals in the Championship, between December and May last season.
The striker also impressed for Denmark during the Under-21 European Championships in Poland earlier this summer, despite his side exiting at the group stages.
The Dane scored twice and assisted two more goals as Denmark's Under-21 side beat the Czech Republic 4-2 in their final group game.
Cardiff have already strengthened in attacking areas this summer by bringing in Danny Ward and Lee Tomlin, and as such Zohore could be allowed to leave for the right price.
However, the Bluebirds boss Neil Warnock and chairman Mehmet Dalman, have insisted will remain in the Welsh capital for the upcoming Championship season, having signed a new contract with the club as recently as April:
"He is not going anywhere. We have a job to do here, he's a huge part of that and he will do a great job for us in the coming season," Dalman told WalesOnline.
"We're going to have a real go at this next season," said Dalman. "Why would we wish to lose our top scorer and without doubt one of our best players?"
Nevertheless Brighton are set to test the Welsh club's resolve by putting in a bid for the Dane in the coming days, as they look to bolster their own attacking line ahead of their debut season.