United are sixth in the Premier League table, 11 points behind Liverpool, and the two sides meet at Old Trafford on Sunday.
Moyes' side have been beaten at home by West Brom, Everton, Newcastle and Tottenham this season, and Fowler says Liverpool should have no fear.
"Teams went there knowing they would be on the back foot and almost expecting to lose. That's not happening anymore.
"Now teams are actually pushing on looking to win there rather than sitting back, hoping to nick a point."
Liverpool have not won at Old Trafford since their famous 4-1 triumph in March 2009, but Fowler believes they are the more daunting opposition these days and is confident they can claim victory on Sunday.
"It's always a massive game but the difference this time is that Liverpool must be favourites," he added.
"I can't remember the last time a Liverpool team went to Old Trafford in that position.
"On paper it's a game Liverpool should win. They're in great form and I am quietly confident Liverpool can get a big result there.
"People talk about how far United have dropped but I also look at it from the other side - how far Liverpool have come.
"That's testament to what Brendan has achieved so far. He has got the team playing so well and I think teams are starting to fear Liverpool again. The manager deserves a lot of credit for that."