Hummels was central to Dortmund's back-to-back Bundesliga titles between 2010 and 2012, and is a mainstay of the German national side - although he has recently fallen out of favour with manager Joachim Lowe.
According to Bild, Dortmund have agreed to give Barcelona permission to talk to Hummels about a potential switch.
The defender is believed to have a release clause worth £29.5 million written into his contract, which Barcelona will meet to seal the deal.
The Catalan giants are in desperate need for a new centre-back, and were linked with a host of big names over the summer.
Carles Puyol has been struggling with injury for some time now leaving the likes of Javier Mascherano and Alex Song, both midfielders, to fill in as cover in his place.
Barcelona were linked with moves for the likes of Thiago Silva, Jan Vertonghen and Daniel Agger over the summer but look to be be trying to avoid the problem dragging on even further by making an early move for Hummels.
Several other clubs are reportedly interested in the former Bayern Munich defender, including Manchester United.
The Old Trafford based club have looked vulnerable at the back this season and could move to bolster their defensive ranks in January.
Both Nemanja Vidic and Rio Ferdinand are nearing the end of their careers and Manchester United could have targeted the younger Hummels as a long-term replacement.
According to Bild, Dortmund have identified Hummels' replacement as Basel's Fabian Schär, who will cost around €5 million.
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