TC himself scored what proved to be his last league goal for the Hammers, in a 1-1 draw, at Villa Park in April 1996 and recent matches between the two sides have been notoriously close, with the last seven Premiership home and away encounters all ending square.
Despite that record, Cottee insists that Saturday's game is one that the Hammers should be looking to win if they are to push up the table and give themselves a chance of ending the season on a high.
"Both teams are in that middle pack," says TC, "and, although every game is important, this is the kind of match that West Ham need to be winning if they are seriously looking to secure a UEFA Cup place through their league position.
"The away form has been poor recently, but sooner or later it has got to change and we do have a good record against Villa down the years.
"When you go away to the likes of Southampton and Bolton, you need to be getting at least a point. We haven't done that recently and it is something that needs to be addressed, because you can't just rely on good home form.
"I think it could be a bit of a mental thing and, once we get a good away win under our belts, I'm sure you will see a few more.
"It's a bit like Newcastle, with their problem in London. For something like four years they couldn't win in the capital, then they go and beat Arsenal and Tottenham on their own grounds within the space of a couple of months. You get a bit of a phobia about it, but it only takes one good result to boost the confidence."
While injuries may be currently taking their toll on the Hammers' squad, Glenn Roeder will certainly welcome the return of Paolo Di Canio, Trevor Sinclair and Sebastien Schemmel from suspension on Saturday, and Cottee believes that the quality is there to enjoy an impressive end to the campaign.
"There were a lot of players missing against Middlesbrough last week, but the team fought hard and managed to secure three very important points," he says.
"The return of Paolo, Trevor and Sebastien will only improve things further and, as long as there are no more injuries, the team can hopefully finish on a high.
"Michael Carrick should be back soon and Ian Pearce's comeback is a big bonus, so there is no reason to be pessimistic about the last 10 games."
Sadly, things aren't so bright for Don Hutchison, a former Upton Park team-mate of Tony's, who faces up to 10 months on the sidelines after rupturing his cruciate ligaments against Middlesbrough last Saturday.
TC offers some words of encouragement, and believes that the condition of pitches nowadays have a lot to do with the kind of innocuous and 'freak' injuries suffered by Hutch.
"It is a big blow for Don and for West Ham. He seemed to just get his studs stuck in the turf and land awkwardly. It is a bad injury but on a positive note he will hopefully come back stronger and fitter.
"Thanks to modern technology, the injury isn't career threatening as it was 15 or 20 years ago, and it has all moved on so much, even in the past couple of years.
"Personally, I think that the pitches have a lot to do with these kind of injuries. They may look lovely, but they are so firm and hard now that, if you get your studs caught in the turf, they can get stuck quite easily and cause these torn ligament injuries that seem to be so common now.
"When the pitches were much softer, you very rarely saw those kind of injuries and think it would benefit all players if they were not so firm."