West Ham will investigate claims that Andy Carroll and Darren Randolph were drunk on Tuesday afternoon.
England striker Carroll, 27, and Republic of Ireland goalkeeper Randolph, 29, had been on a club-sanctioned night out on Monday.
Pictures surfaced on social media on Tuesday of the pair, with users suggesting they appeared drunk.
A West Ham spokesman said: “The club is looking into these allegations and will deal with the players as we see fit.”
Carroll interacted with fans throughout the day, at one point seeming to suggest that he and Randolph were out for coffee, and not drinking.
He tweeted: “I seriously need to sort my parties out!! Sorry lads.
“Back in the day my parties had the wish I was there effect!”
He also retweeted one fan who suggested that people were gullible to believe they were drinking alcohol.
The club have lost five of their six Premier League games this season.
They next face Middlesbrough at their new London Stadium on Saturday at 15:00 BST.