Negotiations have been dragging on since the end of last season between the two parties. However, Barca are confident now of a breakthrough.
Having secured Gerard Pique to a new contract last week, Barca are now pushing to settle terms with Roberto.
RAC1 says Barca aim to extend the midfielder's deal to 2022.
Roberto has established himself as a key member of coach Ernesto Valverde's squad this season, being fielded both at wing-back and in midfield.