The midfielder is expected to hold contract talks with the Spanish side in the summer as he looks for a deal which will see wages equal that of the club’s highest earners.
The 27-year-old’s current contract expires in the June 2019 and he has yet to be told that an extension with improved terms will be offered.
That, according to Sport, has sparked interest from both Manchester clubs and PSG.
The trio have now contacted Barcelona to see if there is any chance of a transfer taking place this summer.
City, who will be coached by Pep Guardiola next season, are said to be particularly keen and willing to spend over £60m for Busquets’ signature.