The stylish centre-half is rated the best young defender in South America and has been watched extensively by Arsenal chief scout Steve Rowley.
Barca are also interested and sports director Andoni Zubizarreta has dispatched his No2 Albert Valentín to Brazil to discuss terms with Sao Paulo.
Rodrigo can play at the back and in midfield - and Zubi's scouts are convinced his style of game will suit Barca's system.
Sao Paulo will be reluctant to sell and it could be that Valentin seeks to negotiate first option for Rodrigo during this week's trip.
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