The Morocco international caught the attention with his performances in the World Cup in the winter, where he helped his side reach the semi-finals before being defeated by France.
There is keen interest in the Sevilla man, with Tottenham Hotspur, Inter and Saudi club Al-Ahli admirers.
Aston Villa are also interested in Bounou and, according to Spanish daily AS, their interest has ramped up in recent days.
Emiliano Martinez could potentially move on from Aston Villa and the Morocco goalkeeper could be an option to replace him.
It is suggested that Sevilla would not be willing to accept offers below €25m.
Saudi Arabian side Al-Ahli would be willing to satisfy Sevilla financially, but it is unclear if Bounou would favour that move.
Bounou, who still has two years left on his current contract, featured in 36 games for Sevilla this season, managing seven clean sheets.