The Daily Mail reported that Fatawu is being considered by the Cherries as a replacement for fellow Ghana international Antoine Semenyo.
Semenyo is on track to join Manchester City when the winter market opens on January 1st, with the Sky Blues prepared to pay his £65 million buyout clause.
Bournemouth have reportedly accepted that the Ghana international is leaving next month and have identified Fatawu as a direct replacement.
Leicester are seeking £30m to sell their attacker in the coming weeks, who has four goals and seven assists in the Championship this season.