Eymael's contract with Ea Lla Koto will expire in June next year, but there is a buyout clause.
According to a source at Stars, the club's management want to tie down the Belgian, who is reportedly on the radar of PSL giants SuperSport United and Kaizer Chiefs.
"There is no secret a few teams both local and outside the country are keen to sign the coach," says the source.
"Both SuperSport United and Kaizer Chiefs are in the picture.
"However, Free State Stars are keen to hold onto the coach for further years than his initial contract."
Eymael has earned plaudits for steering the Bethlehem-based outfit to the Nedbank Cup final and a top-eight finish, a season after they narrowly survived relegation from the topflight.
Stars, in sixth place on the table, will conclude their league campaign with a trip to Orlando Pirates on Saturday before contesting Nedbank Cup honours with Maritzburg United at Cape Town Stadium on May 19.