Jol has come under pressure in the Craven Cottage hot seat, with a poor start to the season leaving them 18th in the Premier League.
New Fulham owner Shahid Khan has professed his commitment to the former Tottenham boss, insisting he will not rush into a hasty decision.
Meulensteen had been linked with the vacant manager's job at Crystal Palace, as well as a senior role at the Qatar Football Club, but the former Manchester United man has instead moved to London.
The 49-year-old departed Old Trafford after Alex Ferguson's retirement, linking up with Guus Hiddink at Anzhi Makhachkala and eventually replacing his compatriot as head coach a fortnight later.
However, his spell in charge of the Dagestan outfit was ended after 16 days, as owner Suleyman Kerimov instigated sweeping budget cuts.
"I was impressed by the vision of Shahid Khan and (chief executive) Alistair Mackintosh," Meulensteen said.
"I've spent many hours talking with Martin Jol and we share a vision of how football should be played and how players should be developed. It's our job to make sure we can bring this vision to life on the pitch for the fans."
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