Mac Allister, who has been linked with a move to Manchester City, explained he had not had direct contact with Liverpool over the decision not to extend his deal.
"We won a Premier League together, we went through difficult times together and I always give my best so we will see what happens," said Mac Allister, who helped Argentina win the 2022 World Cup.
"I don't think I have to prove something - but I have to show the level I can perform and, hopefully, that's the case.
"I love this club. I love the fans. I know very well this is an amazing club and this city has something very special. I love being here."
He added: "There were options to leave this summer. I think right now I'm in the right club and I have the right mindset to give 100% for this club."
Mac Allister was a key part of the Liverpool side that won the Premier League title in 2024-25, but admitted "it wasn't a good season for me individually and for us as a team" as the Reds finished fifth last season and sacked manager Arne Slot.
He made 55 appearances last season for Liverpool, an increase on the 49 games he played in 2024-25.
Andoni Iraola was appointed this summer as Slot's successor and, after using Mac Allister as a substitute in the top-flight opener at Newcastle, has started him in the past two games.
Speaking about Mac Allister's contract, the Spaniard said: "We all have personal situations with different contracts.
"The important thing is he wants to be here. We haven't been together a long time but he has been an important player and I rate him very highly.
"There is still a lot of time to talk about those contract situations."
Asked about Iraola, Mac Allister said: "Since I came to pre-season and worked under Andoni, I could see something special.
"He is a really good coach, he knows very well what he wants to do and we are trying to get there.
"I've not had any conversations with him about [the contract]. But when I see the way he wants us to play and the way we train, I think this can be a successful year."
