The Red Devils became the first and only English team to win all three major trophies in one season in the 1998-99 campaign and are on course to repeat the feat this season.
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"The manager has stressed that he expects to go to the end in all three competitions," Smalling told reporters.
"The FA Cup is notoriously unpredictable. Luton reached the fifth round this year, which shows that anything can happen so there is no point looking too far ahead.
"But our home form has been good and another victory can give us the impetus to kick on and get to another final."
United have won the FA Cup 11 times in their history but have not lifted the trophy since the 2003-04 season, when they saw off lower-league Millwall in the final.
Smalling is surprised by the 19-time league champions' drought in the competition and says it adds further incentive to emerge from their clash with the Royals at Old Trafford victorious.
"I was quite shocked at how long it has been since United won the FA Cup," Smalling admitted. "It is a massive competition and one we all look forward to.
"Before we played West Ham in the third round, the manager stressed how much we wanted to win this tournament. There are quite a lot of lads who haven't won it despite being here for quite a while."