The Hammers are enduring a poor second season under the Croatian and are searching high and wide for new recruits this month.
The club has been linked with moves for a host of players including Sunderland's Jermain Defoe, Brentford's Scott Hogan, Celtic star Moussa Dembele, Chelsea striker Michy Batshuayi and Stoke City's Glen Johnson to name but a few.
Hull City's Robert Snodgrass celebrates
With permanent deals often taking weeks to get over the line at this level, West Ham face a race against time to improve their squad with the required quality up front and at right back.
Bilic and the club's owners will be mindful of the mistakes of last summer where poor recruitment diluted the squad and has been a major factor in the Hammers' fall from grace this season as they find themselves 13th in the Premier League and looking over their shoulders with two huge six-pointers on the horizon against Crystal Palace and Middlesbrough.
Samuel Eto'o has played in the Premier League before
One player being linked with a clutch of clubs who may well come onto Bilic's radar depending on his success in the next week or so is former Barcelona and Chelsea star Samuel Eto'o.
The legendary Cameroonian, who also played in the Premier League for Everton, turns 36 in two months but has proved he still knows where the back of the net is after notching an impressive 25 goals in 42 games for Turkish side Antalyaspor.
While Eto'o is not the kind of long-term investment fans may want to see the club delivering, his record of 336 goals from 695 career games is not to be sniffed at and he is a player who has kept himself in supreme shape.
Bilic has proved age is not a deterrent in his current predicament with the club making Jermain Defoe, who turns 35 this year, his number one target.
Eto'o has been linked with a move to Hull City and Lille but would undoubtedly relish a return to London where he played for West Ham's rivals Chelsea in 2013/14.