The Hammers have been active in the January transfer window already, after bringing in Sam Byram from Leeds United.
And BIlic has suggested today that West Ham could continue to look for more additions in the coming weeks.
To do so, West Ham will have to offload players and it seems that both Zarate and Jelavic could be set to head out of the exit door.
"There are a couple of players who may leave the Club – maybe Zarate maybe Jelavic, and if that happens we will try to get one striker," the Croatian boss said.
Zarate has been linked with a host of clubs in recent times, with Fiorentina said to be leading the race for his signature by the Daily Mail.
The Argentine striker is reportedly willing to take a pay cut to leave the Hammers, and his time at the club seems to be coming to an end.
Jelavic, meanwhile, only joined the Hammers from Hull City in the summer transfer window, but he appears to be heading for a swift exit, without making much of an impact.