Jol is eager to succeed Roy Hodgson at Craven Cottage and the club’s chief executive Alistair Mackintosh is in Amsterdam to finalise the move.
Sources in Holland have stated that he has already agreed personal terms with Fulham.
The 54-year-old former Tottenham manager has two years left on his contract and his departure will require the Cottagers to pay compensation.
However, Ajax are intent on keeping Jol and are still refusing to engage in negotiations with Mackintosh.
It is proving a frustrating courtship for the Europa League finalists, not least because Jol has indicated that he has his heart set on moving to south-west London.
Ajax finished runners-up by one point in the Dutch Eredivisie last season and won the domestic cup.
However, Jol’s relationship with the club’s board has soured over their financial problems, which have seen Serbia striker Marko Pantelic and Denmark winger Dennis Rommedahl allowed to leave.
Holland right-back Gregory van der Wiel and Uruguay striker Luis Suarez are also to be sold with doubts hanging over how much of the money would be made available to the manager to strengthen the squad.
Speaking after Tuesday night’s 7-0 friendly win over amateur side Rijnsburgse Boys, Jol said: “We need to strengthen the squad — everyone knows this — but there’s no money.
“We have lost some good players and no-one is coming in. I fear for the future of Ajax in this position.”
He added: “Ajax know about the offer from Fulham. In the past I have had other offers that no-one knows about. Now in England it is public, but that’s not my fault.”
Fulham remain confident they will capture their preferred choice to lead the club in the post-Hodgson era.
The well-travelled Jol appears to be a good fit at Craven Cottage, not least because he has experience of the Premier League following a three-year spell at White Hart Lane.
In 2006 he led Spurs to the brink of Champions League qualification, with only a defeat by West Ham on the last day of the season dropping them into fifth place.
He was sacked in October the following year after Spurs’ courtship of successor Juande Ramos was unwittingly made public. A solid season at Hamburg followed before he joined Ajax.
Fulham’s squad are currently on their pre-season tour in Sweden — caretaker-boss Ray Lewington is in charge — they face Halmstad today.