Rose went four points clear of the Ibrox Colts, who weren’t playing, with Saturday’s win over Berwick Rangers.
And having already seen off Celtic B on the opening day of the season, Horn’s side are chasing an Old Firm double – hopefully in front of a bumper crowd at New Dundas Park.
But the Rose boss knows his side face a tough game; not too many Lowland League teams have to deal with the demands of players going away on international duty.
"It's going to be really tough,” Horn said. “Looking at their squad there's quite a number of them who have been away on international duty over the past week to 10 days so you don't know really who you're facing.
"But when they're sending guys away on international duty in tells you they've got quality players in their team and they'll be very fit as full-time team and very well drilled and organised because they're training every day,
"They've been playing boys with first-team experience and others who have been out on loan at a decent level
"But we'll just approach it the way we would any other game - they are all big games when you're competing at the top of the table.
"I fully expect them to have more possession, similar to the Celtic game, so it's about how we defend and make it difficult for them but at the same time when we've got the ball to create opportunities for ourselves."
Rose had over 700 people at Saturday’s match with Berwick and Horn is hopeful of an even bigger turnout this week.
He said: “"We're winning at the moment, which gets people coming out to support you, which is fantastic.
"And with Hearts v Hibs not until Sunday you're hoping you might get a wee bit more and obviously playing Rangers as well."