Carroll led the Newcastle attack until joining Liverpool in a blockbuster deal on transfer deadline day three years ago.
West Ham boss Sam Allardyce endured a difficult eight-month spell in charge at St James' Park in 2007, and his assistant manager Neil McDonald also played for the Magpies early in his career.
"If you played for a football club and you are then playing against them you want to get one over on them, don't you?" said McDonald.
"I'm 48 now and I played for them in the 80s but I always want to get one over on Newcastle.
"It is Andy's hometown club of course but at the end of the day we have got another 10 players who will be involved in the game, will be wanting to beat Newcastle and everyone will be doing their best to do that."
Last week's win over Cardiff lifted West Ham out of the Premier League drop zone, and another victory at Upton Park on Saturday would be the first back-to-back triumphs since the Hammers returned to the top flight.
Newcastle have hit a slump having lost their last four games in all competitions, but McDonald warned that Alan Pardew's side should not be underestimated.
"They've had a couple of bad results, but having said all of that they're still in the top half of the league," he said.
"They're still a very, very good team who've got some exciting, dangerous players. We've done our homework on them, we've got a game plan for them, we know their strengths and weaknesses and we have to exploit those weaknesses.
"It goes without saying that it would be six points out of two games and that's certainly what we're trying to do."