The 17-year-old Paraguayan striker has been linked with the likes of Arsenal, Manchester City and Juventus.
The youngster has a clause in his contract allowing him to leave for just £2.5million, according to the Mirror.
Arsenal have a long history of poaching kids from Barcelona and have snapped up Jon Toral, Hector Bellerin, Cesc Fabregas and Fran Merida in the past.
Barcelona are keen for Sanabria to sign a new contract that will keep him at Camp Nou until 2019.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.