The Catalans have made the Frenchman their priority target to replace Neymar, who joined Paris Saint-Germain in a world-record €222m (£198m) deal.
A three-man delegate from Barcelona traveled to Germany earlier in the week to hold talks with the Bundesliga outfit. But they were unable to reach a conclusion after their reported offer of €80m plus €30m in add-ons was rejected by the Dortmund hierarchy.
Dembele has made it clear that he wants to leave the club and join Barcelona after he skipped a training session and also removed the Dortmund moniker from his official Twitter and Instagram accounts. The France international is currently suspended owing to his actions.
According to Spanish publication Sport, Dembele is angry with the club as they have reneged on a promise made to him when he joined them last summer from Rennes. It is believed that the club promised to allow him to leave if one of the big European outfits made an approach, but they are now playing hardball.
The Catalan giants are unwilling to give up as they view the 20-year-old as Neymar's ideal replacement and according to Spanish daily AS, they are ready to make a second bid of around €140m, which is closer to Dortmund's €150m valuation of the player. Barcelona will hope that their second offer is accepted as they are keen to complete the signing before the start of the La Liga season on 18 August.
Barcelona are looking at more than one signing and along with Dembele, they are also keen on signing Liverpool's Philippe Coutinho, who could be viewed as a long-term replacement for Andres Iniesta, who is in the final year of his contract. Barcelona have had one bid turned down by the Reds, who issued a statement that he is not for sale. However, the midfielder is said to have submitted an official transfer request in order to force a move to Camp Nou this summer.