The Daily Mirror claims that Barca coach Pep Guardiola has been looking for a quality left-back for some time now and that he sees Cole as the perfect signing.
Chelsea are reportedly willing to let the 31-year-old go for £12million at the end of this season.
Newly appointed Blues manager Andres Villas-Boas is understood to be open to letting Cole leave as he already has his eye on Porto left-back Alvaro Pereira.
It is thought that Villas-Boas will use the sale of Cole, who controversially moved to Stamford Bridge from Arsenal back in 2006, to help fund a deal for the Uruguay international. The pair worked together during Villas-Boas' days at Porto and he is aware of Pereira's €30million buyout clause.
Meanwhile, Barca president Sandro Rosell will be keen to ensure the club's coach Guardiola remains happy in his role with the Catalans.
The 41-year-old tactician had recently admitted he was not keen to tie himself down to a long contract with Barcelona, and reports in Italy had suggested that Inter Milan owner Massimo Moratti is considering a bid to bring Guardiola to Italy next season.
Rosell responded by saying the club would do its best to hang on to Guardiola, who he called "the best coach in the history of the club".
Barcelona currently lead La Liga after six rounds of fixtures, sharing top spot with Levante, and one point ahead of arch-rivals Real Madrid.