And they are particularly concerned at claims that Carroll and Randolph were still drinking on Tuesday afternoon.
Randolph is facing a £40,000 fine if found guilty. But it is Carroll who would be hit hardest because of his huge salary.
It is understood both men deny being drunk, and the Hammers fan who first made the allegation has since claimed “it was a joke”.
But West Ham, who have lost five of their first six league games this season, are taking the allegations seriously.
The incident is the last thing under-pressure boss Slaven Bilic needs as he battles to stop the slump.
Bilic’s job is not immediately under threat but he has been told he needs to sort things out quickly.