The news comes as Chelsea have been linked with a move for the World Cup winner at the end of the season.
The 24-year-old was successful in Qatar, forming a dominant midfield partnership with Enzo Fernandez on route to winning the whole thing against France in the final.
Sergio Aguero praised his countryman during the tournament, mentioning how his intelligence made him a brilliant player.
He has complemented that international campaign with a very strong club season for the overachieving Brighton.
The Seagulls recently booked a trip to Wembley for the FA Cup semi-final, where they will face Manchester United with a genuine chance at silverware on the horizon.
Mac Allister has enjoyed a prolific season in the Premier League in particular this year. He has seven goals in just 22 games from midfield.
Mac Allister wants to leave Brighton
However, Bailey has claimed he is looking for a move away amid reported interest from some of the best teams in the world.
He said: “Alexis Mac Allister wants to leave Brighton this summer. But he has a lot of hurdles to overcome before he can get out of the AMEX.
“Mac Allister signed a new long-term deal just before Argentina’s World Cup campaign, which saw him excel. And it is no real shock to learn that the interest in him is strong with many clubs around Europe keen.
“However, Brighton as it stands are in no mood to sell – given that he only signed his new deal earlier in the season.”
Chelsea’s interest in Brighton midfielders has not stopped at Mac Allister. They are reportedly still interested in a move for Moises Caicedo after having a bid rejected in January to try and sign him.
With the strong contract situation of both players though, it is likely any move is going to set them back a lot of money.