According to reports in Spain, the Catalan club are 'tired of waiting' for an answer after contacting the 23-year-old's representatives.
Rabiot's contract at Paris Saint-Germain is set to expire at the end of the season, and he has told the Ligue 1 champions that he won't sign an extension.
Barca had reportedly offered a 10 million Euro signing on fee - the equivalent of £8.7 million - and the same sum as an annual salary.
But now they have decided to look elsewhere after the Frenchman's camp failed to get back to them, SportWitness reports.
Liverpool are said to be circling, but football.