Sporting director Deco has held discussions with the midfielder's representatives in recent weeks, with negotiations progressing towards a conclusion.
Barcelona had already decided to address Fariñas' contract situation at the end of August, when he was promoted into Hansi Flick's first-team plans and given a senior squad number.
The talks gathered momentum towards the end of October following his first-team debut, with the club impressed by the youngster's performances.
Fariñas' existing contract runs until 2028, but Barcelona want to reward his progress and ensure his terms reflect his growing importance.
One of the main priorities is to increase his salary, while the club also intends to raise his release clause. His current buyout figure is just €15 million, leaving Barcelona concerned about the possibility of another European club attempting to secure his services.
The proposed agreement would extend his commitment until 2031. A shorter extension until 2030 has also been discussed, although that possibility is understood to be unlikely.
Further discussions are expected after the international break, with only a small number of details reportedly remaining before the agreement can be completed.
Fariñas' renewal forms part of a wider effort by Barcelona to secure the futures of players whose importance has increased considerably.
Raphinha recently extended his contract until 2030, while Xavi Espart has also committed his future to the club until the same year.
Marc Bernal is another player whose renewal remains on the agenda, with an agreement reportedly close to completion.
Barcelona are therefore seeking to protect several members of their squad as they continue to build for the future under Flick.