The former Blackpool boss only took up residence in the Whites' hot-seat in December following the sacking of Gary McAllister.
And after a mid-season blip that reached its nadir in February with consecutive defeats at Huddersfield and Hereford, United have since gone five league games unbeaten to rise back into the League 1 play-off places.
And, in a video interview with Nationwide (available to watch in FourFourTwo.com's interviews section), Grayson believes Leeds can still catch second-placed Peterborough United to claim automatic promotion, before setting his sights further afield to a return to the top flight.
“The club deserves to be in the Premiership,” he said. “We have to try and eventually get back in the Championship, where the club deserves to be at the very least. And then over the next few years you try and progress back into the Premiership. We have to set our sights high.
“We’re on a decent run at the moment. Our first aim is to make sure we’re in the playoffs, but the top two is still catchable for us.”
The Whites have won six home games on the trot, and a victory over Swindon on Saturday will be the first time Leeds have won seven successive matches on their own turf since 1999, when they were in the Premier League.
And Grayson insists such stats don’t add extra pressure, but instead provide inspiration in their quest to return the club to the higher echelons of the football ladder.
“You can always compare teams back to the past. When you’ve got the size and magnitude and tradition of a club like Leeds your always going to draw from history," he said.
"What you have to do is try and inspire yourself to replicate those days, and at this moment in time we’re a long way from that.
“The club has been through a lot of turmoil and it’s going to be a long process, it doesn’t happen overnight.
“The club deserves to be in the Premiership with the facilities and the fan base. Everything is there in place outside of actually being in the next two divisions.”
