The Cottagers set up the mouth-watering home tie on 7th March after beating Championship outfit Swansea in their fifth round replay on Tuesday night.
While most pundits will back Sir Alex Ferguson's side to beat Fulham in this game - especially as they defeated the Cottagers 3-0 at Old Trafford earlier this month - Hodgson believes his team can pull off a shock victory.
"Manchester United, yes, that's a nice bonus, it will be nice to see Sir Alex again," joked Hodgson with a smile.
"It's important for Fulham to be in the quarter-finals, it's been a long while since we have been there.
Not dead"Okay, we've got Manchester United and I suppose people will envisage our demise, but we're not dead yet.
"We've got the game still to play so who knows?"
He added: "Of course we can beat them. We can beat Real Madrid, we can beat Barcelona, we can beat any team you care to mention.
"But if you're asking are the odds on us winning better than the odds on them winning then I think the answer is pretty obviously no. But yes, we can beat them even if they are clear favourites.
"They've played a lot of games this season, they have a lot of things on their mind and maybe we won't be meeting the Manchester United we met the last time.
"How they played against us that night was how we played against Swansea really.
Aggression"Our aggression, our moving of the ball, our goal threat; that was as good as I have seen us really."
Hodgson was full of praise for the club's fans for the support they showed against Swansea and believes the glamour tie against United is just reward for their loyalty.
"What's most important is that it is a very nice cup tie for our fans," he said.
"I thought they were superb from the start against Swansea and they really got caught up in the cup day atmosphere.
"Their support was very, very good and I got the impression they were happy with that they saw.
"It's nice that we've given them a little bit of a bonus with a top match against Manchester United as reward for their support."