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Erling Haaland is reportedly top of Laporta's list of priorities, and talks have already been held regarding the Norwegian's prospective move to the Camp Nou.
He is a player which would appeal to Barcelona, but his huge wages could prevent a deal being struck.
Noussair Mazraoui is also in the final year of his contract at Ajax and would give Barca another option at right-back given that Sergino Dest's future remains uncertain, while Dani Alves is only due to remain with the club until the end of this season.
Meanwhile, Paris Saint Germain prodigy Xavi Simons was another player in the agenda, with the Dutchman having already spent time at Barca's La Masia academy.
The 18-year-old is also willing to see out the remainder of his current deal at the Parc des Princes, and is said to be keen on a return to Catalonia.
However, it has been previously reported that Laporta had no desire to bring the Dutch youngster back to the club. It will be interesting to see if anything changes in that respect in the not-too-distant future.
For now, Xavi will have to make do with the current players at his disposal when his side hosts Elche on Saturday, ahead of a trip to Sevilla on Tuesday before the upcoming Christmas break.