The 27-year-old has made 27 appearances and scored three goals for the Bluebirds since signing on a free transfer from Aston Villa in the summer of 2016.
The Whites, meanwhile, are believed to be in the market for a new left-back since selling Scott Malone to Premier League newcomers Huddersfield Town for £5m earlier this summer.
According to Sky Sports News, Fulham have earmarked Bennett as a key target and will be hoping to recruit him from Cardiff, a club with which they have had dealings in the recent past.
The Cottagers brought Malone in from Cardiff last summer in a deal that saw Jazz Richards move in the opposite direction.
Fulham are yet to win from their opening two Championship games, drawing with Norwich City and Reading.