Modric stunned Spurs by declaring he wants to leave White Hart Lane - and announcing Chelsea as his preferred destination.
However, Tottenham chairman Daniel Levy responded by claiming the midfielder is not for sale "at any price" to any club, with Harry Redknapp stressing Spurs must show Modric they can match his ambition.
Jol was in charge at White Hart Lane from 2004 to 2007, and just missed out on Champions League qualification when they were overtaken by rivals Arsenal on the final day of the 2005-06 campaign.
The Dutchman saw star midfielder Michael Carrick sold to Manchester United that summer, and, shortly before his own departure, claimed he would "rather die" when it was suggested that Bulgaria striker Dimitar Berbatov would also go the same way.
Jol feels his old club must stand firm on the Modric situation if they are to challenge the likes of Manchester City and Liverpool for a place in the Champions League again.
"People always say if you sell Carrick or Berbatov, that you are a selling club. In Holland, it is a complement, but in England it is not," said Jol.
"If Spurs can keep Modric, it would be a big difference and give a good start if they want to be champions or in the top four."
Since being axed by Tottenham, Jol has enjoyed successful spells coaching at the top level in Germany with Hamburg and then in his native Holland at Ajax, who blocked his potential move to Fulham last summer.
The 55-year-old is comfortable with the fresh challenge which awaits on the banks of the Thames.
"For me it was a decision to make, to go back to the Bundesliga, but it had a lot to do with English football, and London. I am ambitious but not over-ambitious," said Jol.
"It all depends on what more rewarding means, because at Ajax they expect you within two years to be in the Champions League, and that is not what they target over here."
Jol may not have long before his first competitive fixture against NSI Runavik of the Faroe Islands on June 30 in the first qualifying round of the Europa League, but feels it will take some time to make his mark on an ageing Fulham squad.
"If you look at the team, it is an older team and they did very well in their own style, and I cannot change that overnight into Total Football with the style we play in Holland," Jol said.
"But in the next couple of months and years, we will try to do something.
"In our style, we have to get the results.
"I need results, but on the other hand want to play good attacking football in an organised way."
Source: Team Talk
Source: Team Talk