Klopp won two Bundesliga titles and a German Cup while in charge of Borussia Dortmund from 2008-15, and has already helped the Reds reach a League Cup final and Europa League semi-final since arriving on Merseyside in October.
And although McAllister concedes there is a lot of work to be done, he sees Leicester City's extraordinary success this season as an example of how quickly things can change in football.
Speaking exclusively in the June 2016 issue of FourFourTwo magazine, the Scots says: “Leicester have shown how far you can shift course in just one year.
"It will be hard for Jurgen to win it next season, but he has the CV and clearly he has the knack of lifting players.
“A lot of people are called ‘winners’ in football when they haven’t won anything. But he has, and I think that there have been enough performances under him that tell me he could do something here. They’ve demolished some really good teams this season. Now they need consistency – but it looks very hopeful.”
McAllister knows a thing or two about winning trophies having been part of the title-winning Leeds side in 1992 and the Liverpool team which lifted the FA Cup, League Cup and UEFA Cup treble in 2001. But when asked which he considers the greater achievement, McAllister admits it is difficult to pick between the two.
“That is a big question,” he says. “There is no doubt that winning the league is the pinnacle in football – playing for your country, too – but winning a domestic league is massive.
“But then again, winning three major cups in a season – who is going to do that again? That was very special and I find it very, very hard to separate them. I guess the thing is that most people at Liverpool would swap that treble for a Premier League title any day.”
Read the full One-on-One interview with Gary McAllister in the June 2016 issue of FourFourTwo magazine. A European Championship special, we chat exclusively to Wayne Rooney, Ross Barkley and Harry Kane about whether this could finally be England’s year, hear from Ashley Williams, Joe Ledley and Ben Davies on the Dragons’ aims in France, speak to Seamus Coleman, James McCarthy and Wes Hoolahan about the Boys in Green’s ambitions, and get the inside track on Northern Ireland from Jonny Evans, Gareth McAuley, Chris Baird and manager Michael O’Neill. If that’s not enough, we recount the best and most bonkers clashes between the five sides from the British Isles and map out each of England’s penalty shootout kicks since 1990. And we haven’t even mentioned our separate 68-page Euro 2016 preview guide yet, featuring even more interviews and everything you need to know about this summer’s extravaganza. Go get it, then subscribe!
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