Moyes spent 11 years on Merseyside before leaving for Old Trafford but the Scotsman now travels 35 miles down the M62 hoping to deny the Toffees a rare double over last year's champions.
Everton, who are just one point off a Champions League spot despite their shock home defeat by Crystal Palace in midweek, have not enjoyed a league double over United since the 1969/70 season.
Looking ahead to Sunday's game, Martinez said: "Facing the champions is a big enough reason to be excited and to make sure we've got the best possible environment at Goodison.
"Having the opportunity to do the double on United is something that is not easy to achieve, and then there is the return of David Moyes.
"We are a club full of integrity and style, we are a proper football club, so we will show the respect to David Moyes for what he's done here."
As for whether the fans will show their ex-boss the proper respect, Martinez added: "I'm sure they will. His job at Everton deserves that. His work has been terrific.
"We all know he's the Manchester United manager now but as a former Everton manager, every Evertonian has got great memories of the job that he did."
Watch Everton v Manchester United live on Sky Sports 1 from 4pm this Sunday