The Catalan giants are banned from signing anyone until the summer of 2015 for breaching regulations regarding the recruitment of young players.
They were previously credited with a strong interest in Gundogan, who first garnered the attention of Europe's elite clubs when helping Dortmund to the Champions League final in 2012.
United have also been linked with the 23-year-old and the Daily Star claims that they are now favourites to sign the German international, who has not played since August because of a back injury.
However, the Red Devils do not seem to have any concerns about his long-term fitness as manager David Moyes has apparently given the go-ahead for them to launch a summer offer for the £25m-rated midfielder.
Dortmund have revealed that Gundogan, who has one year left on his current Westfalenstadion contract, has been offered a new deal to extend his stay with the Bundesliga outfit.