The 24-year-old Croatian has made 34 appearances for the Baggies this season on loan from Benfica and Bilic is eager to extend his stay at The Hawthorns.
Albion are already poised to sign another loan star, Matheus Pereira, in a £9million deal from Sporting Lisbon.
And they are also set to enter negotiations with Benfica over Krovinovic, whose loan agreement does not include an option to buy.
Speaking to Portugeuse newspaper Record, Bilic said: “Regarding Filip , it is not just my decision, because I am just the head coach.
“For me, he is undoubtedly a very important player in our team, but he will also depend on Benfica.
“If you ask me if I want to be with Filip. We love him, he loves being here and, if everything run well, we will end the season where we want to end and we will negotiate with Benfica.
"[Krovinovic] is a very different player from Matheus , although they both play in midfield.
“They have the same attitude and the same qualities. Matheus is more direct , gives more assists, Krovinovic makes everyone around him better players.”