The 24-year-old has been a standout performer for the Seagulls, helping them achieve European qualification for the very first time.
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Mac Allister has had a stellar campaign for both club and country, and won the World Cup with Argentina back in December.
According to TyC Sports journalist Gaston Edul, Liverpool, who have been heavily linked with the star, have won the race for his signature, beating off stiff competition from Chelsea.
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This was also backed up by transfer guru Fabrizio Romano, who claims 'personal terms' have also been agreed.
Brighton chief Barber, who was a guest on talkSPORT Breakfast, was asked about the future of Mac Allister.
"I saw him down on the pitch looking very happy and obviously we want him to be here next season," he said.
"Obviously we know there's going to be a lot of clubs, not just in this country, but around Europe and around the world, that are going to be wanting him to play for them. But, at the moment he's wearing blue and white stripes and I'm delighted about that.
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"If I lost sleep over every report that I read about one of our players doing that then I wouldn't be sleeping very much at all.
"At the moment, he's focused on doing what he can for us during his final two games."
It remains to be seen where the midfielder will be playing his football next season, but he does have a clause in his contract meaning clubs can bypass negotiations if the fee is significant enough.
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It means Liverpool just have to persuade the star Anfield is the right destination, should they offer the asking price for the player.