Mac Allister, 24, was a transfer target for Chelsea and Manchester United but joined the Reds on a permanent transfer from Brighton last week having spoken with Liverpool manager Klopp.
"I had the opportunity to speak with him [Klopp]," Mac Allister said. "It was one of the most important reasons why I took the decision so early in the transfer window. I saw his desire to have me and his desire to continue to win titles for the club, so for me it was very important.
"We spoke about football, his vision and his wish that the club continues to grow and wins championships."
The Argentina international was a key figure for Brighton, scoring 12 goals and setting up three more this past season to help the club secure Europa League qualification for the first time.
Mac Allister, 24, also impressed at the 2022 World Cup in Qatar, starting in all but one of Argentina's matches as they won the competition for the first time since 1986. The former Boca Juniors star is determined to make a big impact at Anfield.
"I'm at a very good stage of my career," Mac Allister said. "I want to make the most of this opportunity. To arrive to one of the biggest clubs in the world and the biggest in England is a great joy and a dream for me. I feel that joining Liverpool was the right step for me to take, not just because of the present but because of the history that it has and the passion that it transmits.
"Liverpool is the Boca [Juniors] of England. I can't wait to play there."
Mac Allister knows it will be tough to compete for honours against Manchester City.
Pep Guardiola's side completed a treble on Saturday, with their first Champions League trophy added to their Premier League and FA Cup successes.
"They show in every game what a great team they are and it's very difficult to beat them," Mac Alister said of City. "Now they will play with the status of being Champions League holders and every team is going to want to beat them more than ever. It's going to be a great rivalry between Liverpool and Manchester City, more than in previous years."
"Decisions are very personal and if he took them, it's because he feels that way and believes it's the best thing for his life and his career," Mac Allister said. "Hopefully, I can enjoy it a lot. It's a league that has been growing and that many players have the desire to play there, so I have no doubts that it will give MLS a leap in quality."