The Red Devils were thumped 4-1 by title rivals Liverpool last weekend and are likely to still be reeling from that result when they arrive in the capital.
Davies believes that could work in the Cottagers' favour as they look to put another dent in United's quintuple dreams.
The Welsh winger admits Fulham will need to be at their best to take a positive result from a fixture which has caused them problems over the years, but is hoping Sir Alex Ferguson's men will have another off-day.
"It's a big ask for United to win it all. When you get to this stage of the season players are going to tire a little bit," Davies told the Daily Star.
"All we can hope is that they've had a little wobble and we can get a result against them, because the pressure is on.
Pressure"Hopefully they won't be so free-flowing with their football. To lose like that against Liverpool means people will be looking at them.
"They don't quite have to prove themselves again, but they've got to bounce back and that puts pressure on. They could be vulnerable."
Fulham's last meeting with United saw them crash to a 4-0 defeat in the FA Cup and Davies admits the Cottagers need to put that performance to the back of their minds if they are to provide more of a challenge on Saturday.
"You just try and forget about games like that," he said.
"It was difficult to watch the video of that one! But you have to get over it quickly."