Barrow, Singleton’s home town club, are top of Kingston Press League One – England’s third division – and have won all their 13 competitive matches this season.
They are the only remaining club with a 100 per cent record and Singleton is expecting Rhinos to be given a run for the money, despite the gulf between the two sides.
Singleton said: “I made my debut in 2011 so whenever there’s been a Cup draw since then I’ve been waiting for this.
“I always wonder if we’ll pull Barrow and this time the stars were aligned and we have. I am glad it’s over here [at Headingley] because I think Craven Park would be a bit of a leveller.
“You take a few of these Aussie boys up there and you never know what you’re going to get!
“But I am chuffed with it and I think it will be good for the town.
“I think at the minute everyone’s buzzing with the form they are in. From what I hear they are in decent form, they are on the rise and attendances are going up.
“I am just looking forward to it and hopefully it is a good day out for the town and a good game.”
Singleton played his junior rugby for the Barrow Island club before signing for Leeds in 2009.
He is familiar with several of the Raiders players from playing with or against them at amateur level.
Winger/full-back Luke Cresswell is among those and Singleton is close mates with Max Wiper and Brett Carter, alongside Brad Marwood, son of Barrow Island coach and ex-Raiders star Dean Marwood.
“Brett and Max are injured at the minute and it’s a shame I’m not going to play against them,” Singleton said.
“But I know them throughout. I played with Olly Wilkes when I was [on loan] over at Wakefield and I feel like they’ve got a strong outfit.
“I’ve been to watch them this year and they are just chewing sides up.
“They are too good for the league they are in – they and Toronto are smashing it.
“They will be in high spirits and they’ll be confident so it’s up to us to sort that out.”
Despite Barrow’s stunning record this year, it – at home to the lowest-ranked team in the competition – was the best-possible draw for Rhinos.
The way Rhinos approach the game will hold the key to how tough it will be.
Against Raiders’ League One rivals Doncaster in the previous round they led 44-4 at the break, but then switched off and were, embarrassingly, out-scored 24-20 in the second half.
“It’s a round further on from the Doncaster game, so the pressure is on a bit more and the crowds start to rise because questions are getting asked about the run we might be on,” Singleton said.
“But Barrow are in form and they are unbeaten so you can’t underestimate them.
“I feel like we need to match them like we would any team, like they are a top-four team in Super League because you never know.
“It’s all on 80 minutes. Some of them might never play at Headingley again and this is like their Grand Final.”
Rhinos are going into the tie in reasonable shape, sitting fourth in Betfred Super League, with a largely fit squad and on the back of a good win at Catalans Dragons.
Rhinos were outplayed for the first 65 minutes in the south of France, but a brilliant late rally turned a 22-12 deficit into a precious 30-24 victory.
“I don’t think that would have got replicated last year,” Singleton admitted.
“I feel like this side has moved on now and last week just showed the character we’ve got and how far we’ve come.
“To come up with a performance like we did midway through that second half is a credit to everyone from one to 17.
“Across the board we are getting to where we want to be, I think.
“We’re not there yet, but I think everyone’s excited about where we could get to.”
Singleton has had mixed experiences in the Challenge Cup and another Wembley appearance is high on his list of targets.
“It means a lot,” Singleton said of the competition Leeds have won 13 times, including back-to-back victories in 2014 and 2015.
“In 2014 I got left out of the final.
“I played leading up to it, but not at Wembley.
“That hurt and I will probably remember that in years to come.
“The year after was my first final and I snuck over for a try, but just in general the form we were in and the confidence we had, I could not envisage us losing that one.
“To be in my first final and for us to play so well, I think we nailed it.
“To listen to the crowd and feel the atmosphere, it was something special.”
Leeds Rhinos: from Golding, Briscoe, Moon, Hall, McGuire, Burrow, Galloway, Parcell, Cuthbertson, Jones-Buchanan, Ward, L Sutcliffe, Delaney, Singleton, Garbutt, Ferres, Handley, Baldwinson, A Sutcliffe.
Barrow Raiders: from Fieldhouse, Fleming, Hulme, Litherland, S Toal, Ashall, Charnock, Bullock, Mossop, Walker, Stack, Morrow, Aspinwall, D Toal, Abram, Brenan, Dawson, Duerden, Cresswell.
Referee: Liam Moore (Wigan).
Kick-off: Tomorrow, 3pm.