The former striker says the club's fans should be careful what they wish for.
He has been writing in his column for London24 today about West Ham's final game of the season against Newcastle United and the subsequent manager decision that needs to be made at the end of the campaign.
The Hammers could end up finishing the season out of the top ten after defeat to Everton at the weekend. At the end of the season it is believed that manager Sam Allardyce could be on his way out of the club, when his current contract ends at Upton Park.
But Cottee is not sure that is the best move for the club:
"We have to match their [Newcastle United's] concentration on the day. We can’t play it like a testimonial game because we will get walloped. They are not a good team and they are lacking in belief at the moment, so we need to take advantage of that and try and get a result, because it is looking like we might even be as low as 12th this season.
"I have been predicting the same score for a while, so why change? I will go for a 1-1. Next week is likely to be D-Day for Sam Allardyce. It has certainly been an up and down season for him and the team, but all I will say about him staying or going is – be careful what you wish for!"
West Ham started the season with a bang under Allardyce but he has struggled in recent times to get the best form out of his players. Individual performances have certainly dropped off in recent times and it is certainly not assured that a change in gaffer will improve their performances.