For now, at least, Spurs have their stories straight and, on Saturday night, Levy and his sporting director Frank Arnesen were singing from the same song-sheet.
'No comment,' is currently the club's official line but, behind the scenes, Spurs have done little to persuade Jol that Tottenham is the place to be.
As Ajax prepare to flex their considerable muscle and remind Jol of their pedigree - as if he needs reminding - Levy has failed to reassure the Spurs supporters that the Dutchman will be hanging around White Hart Lane a little while longer.
The chairman spoke at length with Arnesen on Saturday night about a potential approach from Ajax and they are waiting for the Dutch club to officially register their interest.
Jol, for the time being, is keeping his powder dry. After Spurs' pedestrian performance over Fulham, the club suddenly have European ambitions - UEFA Cup, not Champions League - of their own.
'We were 14th or 15th in the league when I came here and I thought 10th would be good,' said Jol. 'But everyone told me I had to say sixth or seventh, so I will be satisfied if we do something in the FA Cup or play for European football.
'Maybe we won't achieve something this season, but it will be a dream if we are still playing for European football on the last game.'
Jol's dream - like the dreams of George Graham, Glenn Hoddle and David Pleat and Jacques Santini before him - is to rebuild Tottenham and take them into the Champions League.
At Ajax European football is more or less guaranteed. They are third in the league after beating Roda JC yesterday and can secure a place in the Champions League for next season.
Jol, meanwhile, is trying to concentrate on the bread and butter. Inspired substitutions against Chris Coleman's hardworking side paid dividends. Fulham had long since settled for a point by the time Jermain Defoe and the disappointing Mido - all tricks and flicks - were hauled off.
Fredi Kanoute scored the first goal when he won the mind games with Fulham goalkeeper Edwin van der Sar and sent a free-kick spinning into the Dutchman's left-hand corner. Robbie Keane finished Fulham off with a superb solo effort on the stroke of fulltime.
Defeat leaves Coleman's side looking over their shoulders at the relegation battle, but their eight- point lead over Southampton should be enough to see them safe.
' Teams like Palace and Blackburn have it all to do,' Coleman said. 'They are trying to catch us - we're not trying to catch them.
'Two wins would make the world of difference, but there are no panic stations. It was always going to be tight at the bottom and we always have to have one eye on the teams below us.
'Martin Jol has been able to bring a lot of new players to the club. He has spent a bit of money and we can't live with that. We can't pay £4m for a defender - those days have gone for us. They can take two top strikers off and put two on, but there are no excuses from us.'
