The 20-year-old has only been at the club for 12 months, after Dortmund signed him from Rennes last summer.
Although he only managed to score six goals in 32 Bundesliga games, Dembele's performances were enough to impress a number of European clubs.
After selling Neymar to Paris Saint-Germain earlier this month, Barcelona are on the lookout for a replacement.
They had a £90million bid for Philippe Coutinho rejected on Thursday and they are now determined to bring Dembele to the Nou Camp.
Dembele missed training on Thursday without the club's permission, with coach Peter Bosz admitting nobody could get hold of their star forward.
However, reports claim Barcelona are trying their best to finalise the deal before the start of the new season on August 18.