The 29-year-old, who started the season as the Hammers number two behind Adrian, made a series of errors in their 2-2 draw with the Black Cats at the weekend.
Despite the centre-back being 36, there is likely to be a scramble for the signature of the former England captain and Bilic admitted he is one of many admirers of Terry. "He's not only one of the best players in the Premier League but in the whole of Europe".
"He won everything, he did everything and we are talking about an England captain, a true leader". "We will see now in training if he will be ready for Saturday's match".
In an interview with the official site, whufc.com, Bilic said that "He said "I am only frustrated because I have a small injury but I hope to be back for the game against Everton" and we will see that. But, never say never".
But Bilic will be buoyed by the return of key central defender Winston Reid, who has shaken off his own groin problem. In his rehabilitation he did some individual stuff and it's a big boost for us.
Bilic denied the striker's absence was because of a bust-up.
"The rest of the squad, from the game against Sunderland we are without Sam [Byram] who got his red card and without Carroll who will probably be fit for our next game, but this game, no".
"I should know about that if there was because it involves me who spoke with him and everything!"
And according to Italian sports daily Corriere dello Sport, the Hammers are set to make a shock move for Lazio boss Inzaghi as a potential replacement for Bilic in the summer.
"OK, Everton are going to be tough, they are a good side, they have more than enough points and are highly motivated to finish as high as possible and all that, but we are very confident".