Payet scored 12 goals in all competitions last season after joining from Olympique Marseille in June last year.
The Frenchman was also the joint second-top scorer at Euro 2016 with three goals and was named in the team of the tournament.
"I have just seen Payet and he has not played for us since the Chelsea game," Bilic told reporters.
"He has played for France and we will see today. I am expecting him to be fit and ready to start the game. We have missed him. It is the same for every club. France missed him."
Bilic also confirmed that Argentine midfielder Manuel Lanzini, who suffered a knee injury in July, has returned to full fitness.
"Lanzini is fully fit and all the guys who were involved in international duty have not picked up any injuries," Bilic added.
(Reporting by Ian Rodricks in Bengaluru; editing by Clare Lovell)
