The Scottish coach came in to the club to act as number two to his former Liverpool team-mate Steven Gerrard, and is relishing the opportunity to take Rangers in to the group stages of Europe's second-tier club competition for the first time in eight years.
However, the Glasgow-based team will have to get past FC Ufa of the Russian first tier, but McAllister believes that the squad have a good chance of getting to the next round.
Should they reach that stage of the compeition, the likes of Chelsea, Milan, Sevilla or Arsenal could be on their way to Ibrox this season.
"That is where the hunger and desire lies because, if we do manage to make it, there are some fantastic teams in this competition," McAllister said.
"We all associate Rangers — and I hope that is why players come to play here — with big games under the floodlights at Ibrox against one of the big clubs from Serie A or La Liga."
The dream of getting back to the competition could be made or broken on Thursday night, when Rangers play FC Ufa at their home ground.