The Argentine is on international duty and will be playing for his country at the Copa America.
Mac Allister, who signed from Brighton last summer, will be staying with the Reds despite Jurgen Klopp departing the club.
"At one point we gave each other a hug and he told me that it was a shame that we had only shared a year, but it gave me a lot of confidence for the future and everything that comes," said the midfielder.
"He told me what I knew, which was that I was in the right club to continue growing."
Of being at the club, Mac Allister added: "Everything works well, it is not a club with big egos and everyone tries to help you as much as they can.
"On the field everything is different, because everything can be very nice outside, but you have to perform on the inside. I have had to play in various positions and I enjoyed it a lot, I am happy to be in a club as big as Liverpool."