The Whites are keen on strengthening their forward line-up and Daniel Farke has been keen on Paintsil, a player who also attracted attention from Southampton.
Genk have been clear about how much they want to sell the attacker and Leeds failed with an offer.
Leeds submitted a bid worth €10m including add-ons, to the Belgian outfit, which failed to meet their expectations.
Genk got back in touch with Leeds to make a counter proposal.
According to Belgian daily Het Laatste Nieuws, the negotiations for Paintsil have not progressed further as Leeds have not responded to Genk.
There is still time left in the transfer window for Leeds to get back in touch for Paintsil.
However, the Whites appear to be set to keep hold of Willy Gnonto, while Luis Sinisterra may also remain at Elland Road.
