Sven Goran Eriksson and Ottmar Hitzfeld are also on Fulham owner Mohamed Al Fayed's three man shortlist.
Al Fayed insists that the club is not in a hurry to name a successor for Roy Hodgson but chief executive Alistair Mackintosh is under pressure to make the right appointment after the Jol fiasco.
Jol's advisers assured Fulham he had a get-out clause from his Ajax contract but the cheap exit route expired and Al Fayed was unwilling to meet a huge compensation fee and Mackintosh was left red-faced over the affair.
But the move for Hughes will not be straightforward as the Welshman does not get on with Mackintosh from their brief time together at Manchester City.
Hughes will also want to bring his own backroom staff while Fulham want to keep Ray Lewington who has a strong reputation at the club.
Eriksson fancies the Fulham job while Al Fayed has doubts even though he would be Mackintosh's choice.
Former Bayern Munich boss Hitzfeld is also in the frame and was a contender before the club moved for Jol.
Fulham want to make an appointment quickly with the futures of keeper Mark Schwarzer - a target for Arsenal - and striker Bobby Zamora uncertain.
Fulham have already sounded out West Ham about Carlton Cole as they fancy the England striker as a replacement for Zamora but no deal is likely to be rubber stamped until a new manager comes in.