The 17-year-old striker is available for just £2.5m due to a clause in his contract, which has alerted Gunners chief Arsene Wenger.
Barca are desperate to keep the Paraguayan teenager, and are set to step up negotiations to extend his stay at the Camp Nou.
But, with his road into the first-team looking like a rocky one, Sanabria may be tempted by a move to Arsenal.
The London club have a history of nurturing talented young players, and the South American starlet may look to follow the example of Cesc Fabregas.
The midfield ace moved to the Premier League side in the early years of his career and has developed into one of the world’s best midfield players.
Sanabria’s current deal expires in 2015, but Barca are keen to tie him down until at least 2019.
A number of other players have made moves from the Catalan giants and Arsenal have occurred in the past, with talented youngsters such as Fran Merida, Fabregas and most recently Julio Pleguezuelo Selva.
Meanwhile Thierry Henry and Alex Song are two high profile players to have moved in the opposite direction.
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