Mac Allister is expected discuss his future at the club with new Reds boss Andoni Iraola when he returns from his post 2026 FIFA World Cup break in August.
The latest rumours over a possible move to Madrid have been sparked by reports in his native Argentina over Mac Allister allegedly telling his international teammates that he'd played his last game on Merseyside.
Those reports were not backed up, and Alexis' father Carlos has now closed the door on a move away, by insisting his son is keen to work with Iraola in the months ahead.
"We've not spoken to any Real Madrid official, what's being circulated about us holding talks with Real Madrid is not true," he told 365Scores.
"Alexis still has two seasons on his contract with Liverpool.
"Right now, his focus is to get some rest for a few weeks, and then go back to playing in the Premier League, that's the current situation."
Due to the three-week rule relating to player holidays after an international tournament, Mac Allister is not expected back on club duty until mid-August, just under a two weeks before the Reds kick off their new Premier League campaign away at Newcastle United.