The report claims that talks with Gündoğan have reached an advanced stage but there is still disagreement over the transfer fee.
Dortmund are reported to be asking for €40 million but Barcelona do not want to go above €32 million.
Barcelona, who are currently serving a transfer ban, would have to wait until January 2016 to sign the 24-year-old.
Gündoğan has hinted that he may remain at the Bundesliga giants next season.
“That I do not prolong my contract does not necessarily mean that I am gone in the summer.” Gündoğan is quoted as saying by Kicker.
Gündoğan has four assists and three goals in 30 appearances for Dortmund this season.