Following early disappointing performances for the Hammers this season, the Black Star has been relegated to the bench, having made substitute appearances in his last three league games.
Responding to a question suggesting a possible partnership between lead strikers Andy Carroll and Javier 'Chicharito' Hernandez, Bilic discloses that Ayew's peripheral role could soon end.
“I see a lot of potential in that partnership [between Carroll and Chicharito]," Bilic told pressmen on Thursday.
"The key for us is like in one hand we want to get the stability and, if we are talking about conceding goals, then we have to be more stable and have a system with more players at the back.
“But then at the end of the day if you want to get your players who are offensively good on the pitch, it’s not easy to find a system which you can have both in.
“But that is the key and that is what we are looking for and if you’re asking me if I believe in that pair, of course.
“It’s not only them though, we have other good strikers like Andre Ayew and Diafra Sakho. But do I see the potential in that? Yes I do.”
Ayew joined West Ham on a club record deal in summer last year.
His first season, however, did not go as anticipated as an injury left him on the sidelines for about three months following his debut.
But he showed some form of renaissance after the Africa Cup of Nations in February, scoring five times during the second half of the campaign.
This term, the former Marseille man started the club's first three games but disappointing performances have seen him handed bench roles in the last three fixtures.