The 23-year-old featured six times for Argentina in Qatar as he helped them win their first World Cup since 1986.
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Mac Allister started in Sunday's epic final against France, which saw the South American nation win on penalties.
He is the first Seagulls player to lift the famous trophy, with the midfielder earning plaudits over his dazzling displays in the Gulf nation.
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Former Tottenham midfielder Jamie O'Hara has jokingly questioned why Spurs signed his ex-Brighton teammate Yves Bissouma over him in the summer.
Antonio Conte's side are claimed to be interested in the ex-Argentinos Juniors star.
But Barber has declared Brighton are looking to extend his stay at the Amex Stadium beyond 2025.
"We were working on a new contract for Alexis in the build-up to the World Cup," he told talkSPORT.
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"We met Alexis' father [Carlos] several times, he himself played for Argentina with [Diego] Maradona no less, so there's a fantastic family history to playing for their country.
"And obviously he's very proud of his family, he was very excited for Alexis to be going to the World Cup, so nice people, nice family, delighted for Alexis.
"Just as we are for the other Premier League players that took part in Argentina's team last night. Congratulations to them as well."
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And Barber insists no one on the south coast was shocked by Mac Allister's impact in Qatar.
"We felt that Alexis has been performing really well all season, he performed well last season.
"He's been growing into the Premier League ever since he joined us and we were not at all surprised that he was able to make a contribution at that level.
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"Obviously it's never a guarantee that a player as young as Alexis at just 23 is going to start for a country and established as Argentina in a World Cup final.
"But we were confident in him, confident in his ability and also in his character, he's got a very calm presence, he's a really nice lad off the pitch, and a very, very good footballer."
It's likely Brighton will now have to fend off rivals to keep Mac Allister, though, but Barber is prepared.
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"As we've always said, when players do well, when their profile increases, there's always going to be interest in them," he added.
"And this will be no different, Alexis is no different, there was interest in him before the World Cup and I'm sure there will be more interest in him afterwards.
"All we can do in situations where you've got a great asset is to try and protect yourself as best as possible.
"We've done that with several of our players and staff over the last several years, and that's all you can do in these situations.
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"We hope Alexis will continue to be playing for us for some time to come."
Asked what it meant to the club to have Mac Allister return a World Cup winner, Barber added: "Well I think we've been trying to build our profile for a very long time.
"It was only 25 years ago that we were a club that was in the bottom tier of English football, close to going out of business, close to going out of the league.
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"So for a quarter of a century later to have a World Cup winner in our ranks is a fantastic achievement and obviously we are delighted."