Arnautovic has worn the armband in the absence of Mark Noble in recent weeks, and both of West Ham's Premier League goals this season have come from the forward.
The Hammers have lost all four of their Premier League matches this term, however, and Collymore has said that Arnautovic is not the type of player that the supporters should look to for inspiration.
"Marko Arnautovic is the poster boy for the club and Hammers fans need to ask themselves if he is the kind of player the rest of the dressing room is going to follow. I can tell you now the answer is no – because he sets the worst possible example as a player," Collymore wrote in his column for The Mirror.
"His old Stoke [City] team-mate Xherdan Shaqiri can afford to have 20 out of 21 erratic games if he pitches up in that last one and scores two worldies because Liverpool aren't relying on him, he's not the man.
"But Arnautovic is West Ham's top man and if I was in the dressing room and a player like that was the focus, I'd be like, "That's the kind of club I'm at?" What Pellegrini needs to do is tear the whole place apart, get grafters in the side who are going to give you a minimum 8/10 week-in, week-out in terms of work rate, rather than fancy dans."
West Ham will look to avoid a fifth straight Premier League defeat when they travel to Everton on Sunday afternoon.