Wednesday have been strongly linked with a move for the 23-year-old from Leeds, who came through the ranks at Elland Road.
He spent time on loan at Doncaster Rovers during his time at Leeds before making the move to Barnsley in July 2019. He joined Hull on loan six months later before signing a permanent deal in East Yorkshire the following summer.
Wednesday have made five signings so far this window, with all of those players arriving at Hillsborough on free transfers. Wilks would be the first player the Owls have paid a fee for since 2020.
"They have a genuine interest," Kesler told BBC Radio Humberside.
"Mallik is someone who had his good days with us. He is out there training and competing and he will always have a jersey here.
"With all respect to Sheffield Wednesday, the offer is not enough. I think for Mallik it should be higher.
"If they are seeing him at that price level then he better stay here."
Wilks has fallen out of favour at the Tigers, with the forward playing just six minutes of football under Shota Arveladze, who was appointed manager at Hull in January.
Kesler continued: "Negotiations are open. You cannot close the door to anyone.
"For Mallik the offer is not enough, if the offer improves we will consider it, as we would for any of our players."