Moyes was widely lauded for his 11-year spell in charge of the Toffees but Martinez has become an instant hero on Merseyside.
His attacking style of play has been hugely popular and Everton have already surpassed the highest points tally achieved by Moyes in a season with four games left.
The first of those is United's visit on Sunday, and there is far more at stake than simply the return of old faces - former Everton captain Phil Neville is part of Moyes' coaching team while midfielder Marouane Fellaini could also be involved.
Having beaten United at Old Trafford for the first time in the league since 1992, Everton have the chance to end a 44-year wait by doing the double over their rivals.
But most importantly three points would also be a major boost to their hopes of winning the battle with Arsenal for Champions League qualification.
It will no doubt be a source of great pleasure to Everton's fans that it is they rather than United who have a chance of sitting at Europe's top table next season
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 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 and what he's done at our football club.
" I'm sure he will (get a great reception). His job at Everton deserves that. His work has been terrific.
"We all know he's the Manchester United manager now and I'm sure that reception will be very much different but as a former Everton manager, every Evertonian has got great memories of the job that he did."
The warm welcome Martinez expects for the former Evertonians will not extend to the game, though, where the Spaniard wants the visitors to feel as much heat as possible, on and off the pitch.
"This game probably is the most important game of the season," said the Everton boss.
"The roles that Marouane Fellaini and Phil Neville and David Moyes have, they are well-known figures at Everton, they'll always be respected, but they'll be respected after the final whistle.
"Now they're representing Manchester United and that cannot be a nice atmosphere. We all know how important the game is, how vital the three points are. I don't think it's going to be a problem to get the right balance."
The game is even more important for Everton because of Wednesday's surprise loss to Crystal Palace, which ended a seven-game winning run in the league and handed the initiative back to Arsenal in the top-four battle.
Martinez felt his side wanted to win too much and believes they need to appreciate what they have already achieved.
He said: "It's very easy from our point of view. It's making sure we give everything we have and use all the good things we've shown over the last 10 months but in a way that we can enjoy this challenge of fighting to get into the top four.
"I think to be in the fight with four games to go is a remarkable achievement and we can't forget about that.
"We need to play with that enjoyment on our faces and making sure, especially the two home games we have, we really celebrate with our fans and develop a real strong environment and make it as hostile as we can for the opposition."
- Sports & Recreation
- David Moyes
- Marouane Fellaini
- Phil Neville