The Barclays Premier League club have been sent back to the drawing board after top target Martin Jol 'reluctantly' agreed to remain in charge of Dutch giants Ajax.
Jones, who is being heavily linked along with the likes of Mark Hughes and Alan Curbishley, led Cardiff to the play-off final back in May and his success under difficult off-field circumstances in south Wales has also seen him recently linked with vacancies at West Ham and Celtic.
But a statement from Cardiff read: "Neither the club or the manager have received an approach from Fulham Football Club regarding the vacant manager's job at Craven Cottage. As ever, he is 100% concentrating on preparing the team for the new season."