The Daily Mail says Fatawu is being considered by the Cherries as a replacement for 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 accepted that the Ghana international is leaving next month and have identified Fatawu as a direct replacement.
Leicester are seeking £30m to sell the attacker in the coming weeks, who has four goals and seven assists in the Championship this season.