Alan Curbishley, Sven-Goran Eriksson and Mark Hughes are also on the board's list but there is also strong support for a manager who will not disrupt the coaching structure already in place at Craven Cottage.
Hoddle, who was also considered for the West Ham post after Gianfranco Zola was dismissed, is believed to be interested despite his commitments to his own football academy in southern Spain.
The 52-year-old former Tottenham boss has not returned to management since stepping down as Wolverhampton Wanderers boss in July 2006 but he is still regarded as an original thinker with a strong coaching reputation.