The Hammers are enduring a tough second season under Bilic, not helped by star player Dimitri Payet going on strike last week.
Payet is reported to be demanding West Ham sell him back to former club Marseille so he can return to France for family reasons.
But regardless of what happens over his future Bilic has been desperate to bring in new signings anyway with the club struggling to build on their fantastic season last term.
The East Londoners have been linked with countless players from Sunderland's Jermain Defoe to Hull City's Robert Snodgrass.
Arsenal's Francis Coquelin
But could Bilic be tempted to test the waters with a move for Arsenal midfield ace Francis Coquelin in the summer after former Gunners star turned Sky Sports pundit Charlie Nicholas delivered a damning verdict on the Frenchman's future at the Emirates.
“I’m not his greatest fan, but they don’t have many options in that position," Nicholas told Sky Sports.
West Ham United manager Slaven Bilic
“He’ll do a job short term and after that you’d think they'd get a decent price for him.
"It puts his value up and I would sell him in the summer when everybody is fit.”
A move for a player like Coquelin could see Bilic find a natural replacement for Alex Song who was superb in spells playing that holding role for West Ham.
Now plying his trade for Rubin Kazan in Russia, the African has a lot in common with Coquelin from the fact they both came to prominence at Arsenal, were both loaned to Charlton to cut their teeth and both play the same position.
Should Arsenal take Nicholas' advice and sell Coquelin, they would likely want over £15 million for the player in the current market.
That should not be too much of a problem for West Ham, though, given their increased financial clout following the move to the Olympic Stadium - where they have 52,000 season ticket holders, the second highest in the Premier League behind Manchester United.