The club have already signed both Leandro Castan and Dodo from Corinthians, and are seeking to bolster their back-line further with the acquisition of the 25-year-old.
Negotiations are currently at a stand-still, with the Brazilian club holding out for €15 million, and the Giallorossi prepared to offer a maximum of €12m.
Rhodolfo, whose current contract expires in 2016, has made 12 appearances this season, and featured in Sao Paulo's 2-0 win over Bahia in the Copa Sudamericana on Thursday.
The Italian side's sporting director, Walter Sabatini, is said to be working on the deal over the weekend, with progress expected to be made between the two parties on Monday.
The club are considering other alternatives should a deal fail to materialise, and have their eye on Twente's Douglas, Gremio's 21-year-old defender Saimon and Brazil's Olympic star Bruno Uvini.
Roma open their Serie A campaign against Catania on August 26.
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