The Sky Blues are potentially 90 minutes away from their first Irish Cup final since winning the competition in 1989 – the club's last major trophy success.
But they face a tough test in the shape of Portadown in Saturday's semi-final at Windsor Park (5.30pm).
"From the very first game against Ards, I have told the players to dare to dream, to imagine walking out at Windsor Park on May 8," Walker told Times Sport.
"The cup has been of major importance to our season and I'm really pleased with the character we have shown in the competition.
"Portadown will be favourites – they have an experienced side whereas we're relatively inexperienced when it comes to occasions like this – so we have to bring our 'A' game on the day.
"The games between us have been pretty close so we have to be brave and prepared to go forward a wee bit more and play with a panache and try and express ourselves at Windsor."
Walker will run the rule over his injured players this week, while also having to prepare a team for tonight's (Tuesday, 7.45pm) Carling Premiership home 'derby' against Coleraine.
"We have one or two bumps after Saturday. Gavin Taggart is suspended for the Coleraine game which makes him eligible for the semi-final but he took a knock to the knee in block tackle at the weekend, although he has the best part of a week to recover.
"Mark Surgenor limped off at half-time with a calf strain which is a bit of a concern, so we have one or two in sick bay.
"We'll bring Kevin Kelbie over on Thursday this week – he's still bothered by a shoulder injury and there's no point bringing him over on Tuesday if he's not playing.
"Michael Smith was rested on Saturday - he has had a bad foot which has required painkilling injections and also he had family over from Canada so we thought he had earned a rest."
Smith is the most obvious replacement on the right side of midfield for winger Gary Muir, who is ineligible for United in the Irish Cup, having signed after the deadline for registering players in the competition.
Walker is not fazed by the tea-time kick-off, which is to facilitate live coverage of the match on Setanta Sports.
"We'll encourage the boys to lie late on Saturday morning and then meet in Belfast for a bit of a loosener and a bit of set-piece work – I have a few ideas on variations on that.
"We're going to the Park Avenue to eat and for our team talk.
"The preparation will be different but that will be no bad thing because the very fact that the preparation is different is because it's not an ordinary, run-of-the-mill game," added Roy.
n See page 55 for full semi-final preview including ticket details.