With both Andy Carroll and Diafra Sakho sidelined through injury and Mauro Zarate closing in on a deal to join Fiorentina, Bilic is keen to bolster his attacking options in the transfer window.
But the Hammers boss has dismissed speculation that Sturridge, the England striker who has featured just six times for the Reds this season due to a string of injuries, is poised for east London.
“I am not talking about who we want – Daniel Sturridge is a big player and a big name – but that is only paper talk.”
Sturridge has not trained with the Liverpool squad in six weeks, and manager Jurgen Klopp is reported to be growing increasingly frustrated with the situation.
But when it was put to Bilic that Sturridge, 26, may become available, the West Ham boss replied: “What if? I would take Lionel Messi also, but it is only an ‘if’ so there is nothing in it.”
Bilic said Sakho, who this week was involved in a car accident, and Carroll are both “ahead of schedule” on their return from injury and are expected to be available in mid-February.
But the Croat revealed he remains interested in signing another striker with Nikica Jelavic, who scored in the 2-1 defeat at Newcastle on Saturday, possibly leaving the club in January.
“We are not panicking,” added Bilic. “We know that we have a couple of players that are injured. “On the other hand there are a couple of players that may leave the club. Maybe Zarate, maybe Jelavic and if that happens, and it may happen, then we are going to try and get one striker.”