The 25-year-old joined the Reds from Brighton & Hove Albion last summer for an initial £35m, which could rise to a fee in excess of £50m with add-ons.
Mac Allister established himself as a first-team regular under Jurgen Klopp in his final season as Liverpool manager, with the midfielder starting 40 of his 46 appearances across all competitions and contributing with seven goals and seven assists.
The Argentina international played a key role in helping his country retain their Copa America title earlier this month and he will soon report back to Liverpool for pre-season training under new head coach Arne Slot.
Mac Allister has a contract at Anfield until June 2028, but recent reports have suggested that La Liga giants Real Madrid could swoop for the midfielder and trigger a 'secret' €70m (£60m) release clause in his deal.
Mac Allister's father denies Real Madrid 'negotiations'
However, Mac Allister's father has since played down rumours of his son joining Real Madrid and has confirmed that Liverpool's No.10 will remain on Merseyside for the 2024-25 campaign.
"Alexis is performing very well at Liverpool, and this is the important thing to say at the moment," Carlos Mac Allister told Egyptian news outlet MSR.
"There are no negotiations from Real Madrid with Alexis, and the player will continue with Liverpool next season. If future offers arrive to sign Alexis, we will discuss them with Liverpool's management first."
The Liverpool midfielder himself has insisted that he is content at the club, telling ESPN Argentina in May: "I don't talk about assumptions, I'm very happy at Liverpool.
"I think it was a good season individually, then we had some objectives that we couldn't meet, but I still think it was a very good season."
Mac Allister "happy" at Liverpool
In a separate interview with Argentina news outlet TyC Sports last month, 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."
Mac Allister, who predominantly played as a deep-lying playmaker last season rather than in his preferred position further forward, is expected to feature regular under new boss Slot next season, even though Liverpool are believed to be on the lookout for a new midfielder.
Real Madrid, meanwhile, have seen Toni Kroos depart and retire from football, but they are still well stocked in the midfield department, with Jude Bellingham, Aurelien Tchouameni, Federico Valverde, Eduardo Camavinga, Arda Guler and Dani Ceballos all at Carlo Ancelotti's disposal, while 38-year-old Luka Modric has extended his contract to stay for another season.