Eymael was linked with the Cranes earlier this year, and a source says the Ugandan Football Association (FUFA) is determined to get the Belgian on board.
"Gordon Igesund [former Bafana Bafana coach] was also in the race but Eymael is in the front. The only problem with Luc is that he wants to come with his assistants yet FUFA want to retain Moses Basena as his assistant. That's the only hiccup," the informant tells KickOff.com.
However, Eymael insists he is staying put, having only joined Stars in late August on a two-year deal at the expense of Sammy Troughton.
"I'm not aware, I haven't been contacted. There was contact before I came to Free State Stars. What I can tell you is that I'm happy here, simple. I just want to focus on my career here. I can assure you that I will not leave here," he says.
Ea Lla Koto general manager Rantsi Mokoena says Eymael remains at the helm in Bethlehem.
"I don't know, as far as I am concerned he is our coach. I don't know anything about that," Mokoena says.
Stars are sixth in the Premiership standings with 19 points from 14 matches heading into their final game of the year against Orlando Pirates at Goble Park on Saturday (18h00).