Gündoğan did however, only recently extend his contract with the Germany international of Turkish origin and has another two-years left on his contract.
The 24-year-old midfielder would join Arda Turan as the second ethnic Turkish player in the reigning La Liga champions squad should he end up joining over the winter transfer period.
Barcelona are expected to make a transfer over the transfer window to bring in reinforcements for the injured Rafinha.
The Champions League title holders will be able to sign and register players in January due to the FIFA transfer ban coming to an end.
Barcelona could face competition from Manchester United who remain interested in Gündoğan according to the Daily Express.
Dortmund rejected an approach from United just before the end of the summer window for Gündoğan according to the German newspaper Express.
Gündoğan previously turned down a contract offer from Dortmund but changed his mind regarding his future following discussions with their newly appointed manager Thomas Tuchel.
The 24-year-old wrapped up the season with five assists and three goals in 33 appearances in all competitions.