Fulham sacked Ranieri yesterday after a dismal spell at Craven Cottage.
The Daily Star says Clarke could be the man they choose to get them back in the big time next season.
Clarke was a target for the Cottagers back in 2015 but decided to remain at rivals Reading.
Fulham have since been bought over but there remain influential figures at Craven Cottage who are big fans of Clarke.
Scott Parker has been handed the reins to the end of the season.