Kouyate has been with Anderlecht since 2008, but reports in Belgium suggest the club are expecting the Senegal international to leave this summer.
He is due to receive a Belgian passport in the next few days, which would remove one potential obstacle to a move to England.
The 23-year-old was linked with Newcastle United and Southampton at the end of last season, while Dynamo Kiev have also shown an interest.
However, Kouyate is not expected to follow former Anderlecht team-mate Dieumerci Mbokani to Ukraine and his agent Tedir Bekir is waiting for a decision to be made.
"I won't give any names, but Cheikhou has contacts with clubs from the middle of the table in England," Bekir told La Derniere Heure.
"He hasn't made a choice yet. The right balance between the sporting challenge, family and finances has to be found."