Arsene Wenger is believed to be in the market for a midfielder after bidding £10m for Newcastle midfielder Yohan Cabaye.
It was reported by the Mirror last week that Arsenal were prepared to meet the demands of Sevilla for the 20-year-old.
It now appears that Arsenal again moved too slowly in the transfer market after the player's representatives flew to Monaco to thrash out terms on a long-term deal.
Arsenal's hesitation may be due to the situation surrounding Mathieu Flamini, who plays in a similar position Kondogbia. According to reports the Frenchman is set to re-sign for the club on a free transfer.
French newspaper Le Parisien reported that Monaco met the release clause of €20m and Sevilla had no choice but to acquiesce.
Monaco are continuing their summer spending spree after spending well over €100m so far.
They have been looking for reinforcements in the defensive midfield position with Jeremy Toulalan representing their soul player currently fulfilling that role.
Kondogbia, who won his first senior cap for France recently, is seem as the perfect partner for Toulalan by Monaco manager Claudio Ranieri.
Sevilla have acted quickly to replace the coveted midfielder by signing QPR's Stephen M'Bia on loan.