The midfielder has enjoyed incredible success with the footballing icon as they both played key roles in Argentina's World Cup triumph last year.
But while the 24-year-old appears comfortable playing alongside the seven-time Ballon d'Or winner now, he admits he was petrified when he first met him while on international duty.
"I was so nervous and I think it was a friendly in Spain and Messi was there having dinner and I was shaking," he said on GOAL's Box to Box when asked about his first meeting with Messi.
"And as you can see, I'm red or ginger, so in that moment I was even more and shaking. But then, as I said, he's a very nice guy, so when you have the possibility to know and meet him, he's a very nice guy."
The debate continues to rage on about who is the best player of all time, with many citing fellow Argentine Diego Maradona or Portugal hero Cristiano Ronaldo as challengers to the title.
Although Mac Allister's father, Carlos, played alongside Maradona, the Liverpool player believes it is his national team-mate who will be remembered as the best to ever grace the field.
"No, I think it's Messi. Of course, I haven't had the possibility to watch Maradona on live, but for me, Messi is the best and he will be the best forever," he added.
The former Argentinos Juniors star has enjoyed a bright start to life at Liverpool after joining from Brighton in the summer window and he is happy to be playing under Jurgen Klopp.
"I can already see that intensity and I can see what he wants from me and from the team," he said. So he's one of the best manager in the world. I was really looking forward to it and now I'm really enjoying it."
He added: "It's a dream come true, what you dream when you are a kid. Not just Liverpool, of course, the biggest teams in the world, and I think Liverpool is one of them. In this amazing stadium, I had the possibility to play as an away player and it was fantastic.
"Then I had my debut with this team. It wasn't maybe the best because I got sent off, but still, that atmosphere that the fans create there is amazing."
Check out the full episode of Box to Box on GOAL's YouTube Channel.