The 23-year-old striker has been in form having scored four goals in two games, but he missed Tuesday night's EFL Cup third-round defeat to Norwich City.
On Saturday, Everton travel to the coast to take on Bournemouth at the Vitality Stadium, and Koeman is hopeful of having Lukaku in his lineup.
"He did training, separate to the group, today and we expect him to train normally tomorrow morning," Koeman told reporters. "If that happens then he is fit for the weekend."
Everton are unbeaten in the Premier League so far, having won four and drawn one of their games this season.