The Hammers have claimed some famous victories already this season.
"Let's be honest. West Ham are behind the three main London clubs. Arsenal, Chelsea and Spurs have all had Champions League experience of various forms," he said.
"West Ham are the fourth London club at the moment. As a passionate West Ham fan I want us to move on to the next level and be competing with them.
"But Slaven Bilic is doing a great job, and if we build slowly I think West Ham can get to that stage. People will laugh and say West Ham fans are dreaming but you have to dream in football," he added.
The Boleyn Ground outfit currently sit sixth in the Premier League table, having already beaten Arsenal, Liverpool, Manchester City and Chelsea this season.
And while their performances in those games would suggest that Cottee's prediction is not as bold as it initially sounds, defeat against the likes of Bournemouth and Watford have prevented Bilic's men from staying in touch with the current top four.
However, with tenth-place Stoke City being the highest placed side that the Hammers will come up against during the busy Christmas period, Bilic's men will have the opportunity to prove whether they have banished the complacency which prevented them hitting the heights they hit against some of the division's biggest sides.
Although Cottee's prediction will arguably come too soon to be fulfilled this season, a string of ruthless performances in December may well put them back into the mix to spring another surprise during this bizarre campaign.