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.
Fellaini has become an increasingly influential player for Everton since they recruited him from Standard Liege in 2008 for a record fee of £15million, and reports have suggested several major Premier League clubs are interested in making a move for him.
Chelsea are among those to have been linked with a move but Fellaini has been careful not to fan the flames.
He was this week quoted by Sport Wereld as saying: "I heard about that interest, but I've never really talked with Chelsea.
"In all seasons, there is talk on the grapevine about other clubs, but I was never personally around the table with another club.
"If Chelsea want me, they can cross that bridge, but for now I'm happy at Everton.
"If we finish in fourth place we will qualify for the Champions League and we are currently fifth."
Asked if he thought it would be better to play in the Champions League with Everton rather than Chelsea, Fellaini said: "Maybe, because Everton launched me in England.
"After this season I still have three years left on my contract and the club has become a bit like my family.
"I have a tremendously good relationship with the manager and my team-mates.
"People talk all the time about Chelsea like I've already signed. I am still an Everton player. "
Phil Jagielka is expected to be involved for Everton on Sunday despite sitting out England's 2-1 victory against Brazil, while fellow defenders Seamus Coleman (thigh) and Tony Hibbert (calf) remain sidelined.