But, despite the clubs having gone down very different paths since they regularly fought each other at the top of the Premier League, Naylor is adamant the rivalry and ill-feeling between them still exists.
"It's a big game and, after growing up a Leeds fan with all the history, you don't like them very much," the 32-year-old said. "There's not much love for Manchester United, obviously.
"But I don't hate them and they've gone on to great things whereas us, as a club, have struggled over the last few years.
"If you ask any of their players that have been at the club a long time, the likes of Gary Neville, he will know the history between us and I'm sure he's got no love for Leeds United and vice versa."
Naylor joined his hometown club a year ago and, along with Grayson, has played a key role in helping them go some way to restoring their reputation after a turbulent spell which saw them slide from Champions League semi-finalists to the bottom side in League One.
And the former Ipswich defender, who was at Bramall Lane in 1992 to see Leeds pip Manchester United to the First Division title, is confident the two sides will soon be meeting again in the top flight.
"We've got the most loyal supporters in the country," he said. "They've stuck with us through the lean times and a game like this is a big thing for them and a reward for some of the places we've had to go over the past couple of years.
"It's a good thing but we want to do it week in, week out. It's where this club and the fans deserve to be. You ask any Leeds fan and they'll say we're as big as Manchester United."
Man. Utd v Leeds. Click here to bet.