The Premier League new-boys are seeking a new wide-midfield addition and Fatawu is under consideration, says BBC Sport.
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The Ghana international, 21, is rated in the £30m class by the Foxes.
Along with Sunderland, Everton are also interested in Fatawu.
Everton are turning to Fatawu after being frustrated in their attempt to land Southampton winger Tyler Dibling.
The Blues had an offer of £27m rejected by Saints earlier this month.