The World Cup winner became the first of four midfield signings for the Reds at the start of the summer and has wasted no time establishing himself in the side.
It has by no means been plain sailing, having been sent off during the first home game of the season against Bournemouth and being substituted after a difficult opening 45 minutes at Wolves.
That doesnt appear to have worried the boss too much, with Mac Allister revealing that his strong relationship with Klopp has been the subject of playful taunts from his peers.
Many of my teammates tease me because they say that [Klopp] is my dad now. The relationship with him is perfect, he is a very charismatic person, who always tries to be close to the players, the midfielder told La Nacion.
He has crazy moments that you might see in a game, and you cant stop laughing. For me it is a pleasure to be able to work with him.
Mac Allister has started all five of Liverpools Premier League games in the campaign so far having impressed throughout pre-season by slotting in seamlessly to his new surroundings.
It is not the first time he has faced jibes from colleagues, having admitted in an interview with The Athletic last year that Argentina captain Lionel Messi asked members of the national squad to refrain from calling him ginger.
The 24-year-old looks to have followed in the footsteps of fellow midfielder Adam Lallana, who was the self-proclaimed teachers pet during his time at Anfield.
He explained that his surprise inclusion in the starting lineup at Molineux, while South American duo Luis Diaz and Darwin Nunez were named on the bench, was part of the reason for the new reputation he has picked up.
The last game we returned from the national team I was the only South American who started; well, Ali also did, but he had not played in Brazil. Lucho [Diaz] and Darwin were on the bench, he continued.
Then they told me that he is my dad, that he cant take me out, that I had played all the games and so they drove me crazy!
But beyond the joke, he is a person that I respect very much and I hope that he continues like this and that I can continue learning from him on the pitch.