Fellaini - the Toffees' top-scorer this season with 11 goals in all competitions - was outstanding against United in August, netting the winner as his side got their 2012-13 top-flight campaign under way with a 1-0 victory at Goodison Park.
He also scored last term in a 4-4 draw between the two clubs in Manchester, which dealt what proved to be a major blow to the hosts' unsuccessful title bid.
Last Saturday Fellaini came to Everton's rescue with a brace to secure a 3-3 home draw with Aston Villa, and Moyes is optimistic the 25-year-old can again cause United, the current league leaders, plenty of problems on Sunday at Old Trafford.
"He is coming back into a little bit of form," Moyes, whose team are fifth in the table, said.
"He scored a couple of goals for us last week and he is the sort of player who seems to enjoy the bigger games."
Fellaini has been nursing a hip injury and did not play in Belgium's midweek 2-1 friendly win against Slovakia, but Moyes expects him to be fit for Sunday's game.
"He has got really bad bruising, but I think he will be okay," the Scot said.
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