United went out of the competition at this stage last year against Portsmouth.
Hodgson told Sky Sports: “It’s a big cup match as we’ve reached the quarter-final stage and the beauty of the cup is that you’re never completely out of it.
“We’ve got home advantage against the champions of England, and we believe we can make a game of this. We’re hoping it’s going to be our day. If we did want to take some solace then it is there in Portsmouth last year.
“I’m pretty sure that if we look in the record books we could find some other interesting results.
“Look at Barnsley knocking out Liverpool at Anfield last year. We know that in the cup all is possible so we go in as underdogs as most teams do when they play Manchester United.
“That must be a hard burden for Sir Alex and United to bear as whoever they play they are always the favourites. But that doesn’t mean that as underdogs we think we have no chance. We believe that if we do what we can and need to do, it can be our day.”