The club is in something of a crisis with the owners and manager at loggerheads in a rather public spat while the Hammers board have also been exchanging pleasantries with their Sporting Lisbon equivalents over the doomed transfer of William Carvalho.
Speculation has been rife over Bilic's future with reports claiming he will be the next to go after Frank de Boer's dismissal at Crystal Palace.
A large section of Hammers fans accept Bilic must do better but blame the board for the mess the club finds itself in and what they feel is one PR disaster after another.
Many accuse David Sullivan and David Gold of signing players rather than the manager, with the disastrous £10million January acquisition of Scotland international Robert Snodgrass cited as a prime example.
"Allegedlly Bilic has asked a Premier League player in Robert Snodgrass where does he play," Barton said on talkSPORT.
"I mean you have to worry if the manager's lack of knowledge is that evident.
"Even if I never signed Robert Snodgrass (as a manager) I would still be aware of what's going on in the league around me, certainly the teams I'm playing.
"Maybe not aware of every incident in world football but if he doesn't know what's happening with Robert Snodgrass, playing in the league he's competing in, you have to worry about Bilic's ability to conduct the job in the strongest fashion for West Ham to move forward."
Robert Snodgrass is substituted by Slaven Bilic last season
Snodgrass claimed Bilic played him out of position during his time in East London.
The midfielder's comments certainly haven't helped Bilic's standing among supporters at a time when the manager finds himself under intense pressure.
But Barton makes a salient point, any top manager would be expected to know most of the players in the league, particularly one his team had just spent £10m on after he had scored seven goals and provided as many assists for Hull City leading up to the move.