The Press Association and the BBC are amongst those reporting that the fee has been agreed for the Arsenal captain.
Manchester United were also keen on the 28-year-old Belgium international but Arsene Wenger admitted that he did not wish to sell the player to a Premier League rival.
It is believed that United ended their interest when Arsenal asked for a player in part exchange.
"Ideally, yes, we would like to sell him abroad and that is an option for us," Wenger said on Thursday.
The Belgium defender could complete his move to the Nou Camp over the weekend although he has still to agree personal terms and complete a medical.
If the deal is completed it will be the second defensive addition of the transfer window by Barcelona.
Last month they confirmed the signing of Valencia's French defender Jeremy Mathieu for €20m.
- Sports & Recreation
- Arsene Wenger
- Manchester United