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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?