Liverpool striker Sturridge missed last Sunday’s home game against Crystal Palace with a hip problem, continuing a miserable run of injuries that has limited him to five league starts this season after making 18 in the previous two campaigns.
He has been well aware, since last summer, that he does not fit into the plans of boss Jurgen Klopp.
Although he appeared as a second-half substitute in the wins over West Brom and Stoke this month, the 27-year-old is not expected to feature again for the rest of the season and may have kicked his last ball for the Anfield giants.
Asked about the marksman, Bilic said: “We are going to see. We have our list of strikers.
“If you talk about him as a player, especially if you go back two or three seasons he was unbelievable. But [at the time] he wasn’t a subject for West Ham.
“Now he plays very rarely, but I watched Stoke against Liverpool the other day. He came on and, with a couple of passes, he broke their defence. He split them up some great passing.
“So of course he is showing that when he plays — but he plays very rarely.
“They have a lot of quality there and I don’t like to comment on the decisions of other managers.
“I don’t know the situation there. I don’t see their training. I’ve just seen enough of their games to know that when they are fit they are doing well. Especially in that area with Mane, Coutinho and Lallana.
“So what can I say?
“When he is on fire, [Sturridge] is a great player.”
West Ham have had been riven with fitness issues of their own up front this season.
Andy Carroll has started only 15 league games and will remain on the sidelines for the trip to Stoke this weekend with a groin problem, while fellow frontman Diafra Sakho , who has managed just four appearances all season, is also a doubt.
Their £20m record buy Andre Ayew also missed two months after picking up a thigh problem on his debut for the club last August.
Asked whether any summer replacement for either man needs to be more durable, Bilic said: “I’m Andy’s biggest fan.
“It’s not a coincidence that when we won six games out of nine he was fit, he played, he trained and the team around him knew that he is there. That’s how big a blow it is when you are without him.
“And when you are without Sakho as well, you are not going to win six out of nine. It’s all related, the only thing about Andy is how many games he is going to be available.”
Bilic also confirmed his players remain well aware they are banned from gambling, following Joey Barton’s 18-month suspension on Wednesday for placing bets.
“I haven’t reminded them. The players know it is a rule, like the rule that you can’t use your hands on the pitch,” he said.
“You can’t be involved in any sort of gambling, the players should know and they do – you don’t have to remind them.”