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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.