The former Hammers forward cannot see his old side losing against Manchester United.
Both sides square off at the Theatre of Dreams later today as Slaven Bilic's men look to build on an already brilliant season by reaching the semi-finals of the world's oldest cup competition.
Old Trafford has long been one of the most daunting locations in English football by virtue of the Red Devils' utter dominance over the last two decades.
But with West Ham - fifth in the Premier League table and two points behind Manchester City in the race for Champions League qualification - punching well above their weight all season long, Cottee is optimistic they will continue to do so at the Theatre of Dreams.
I'm off to Old Trafford as a fan 2day. Don't want to get too excited but I think we'll get at least a draw !#COYI— Tony Cottee (@TonyCottee9) March 13, 2016
In August, it would have been unthinkable for West Ham fans to feel confident about their side's hopes of beating United on their own turf, but these are the times that Bilic has built.
The Croat has been an excellent appointment in East London, and even he will fancy his team's chances of extending the feel-good mood this afternoon.