The defender was linked with Newcastle United and Southampton at the end of last season, but Dynamo Kiev were also reported to be interested in signing the Senegal-born player.
Arsenal was also mooted as a possible destination for Kouyate, 23, a year ago while Lyon and Marseille are now rumoured to be looking in his direction.
Kouyate had already declared that he planned to leave Anderlecht before the end of last season, and he is not hiding the level of his ambitions.
"We are all ambitious," he said. "I want to move in my career. If I improve big clubs from abroad will come for me.
"The story of Arsenal was true but nothing materialised. Arsene Wenger is a great coach and to show an interest in me was fantastic.
"Newcastle could be great as well, but let's wait and see."