The 49-year-old Dutchman was taken on board at Craven Cottage last month with the Whites floundering in the Premier League.
It has been suggested that Meulensteen was brought in by new owner Shahid Khan to relieve his compatriot, but the former Manchester United coach has strongly refuted those rumours.
"People can think what they want, but it definitely was not the case that I came in to take over," the new boss told BBC Sport. "The reason I came was to work alongside Martin Jol. We were trying to take Fulham to the next step.
"I spoke to Martin Jol straight away [after he was sacked]. We had a long conversation, for maybe 30 minutes.
"There are no hard feelings between him and myself. We have known each other for more than 25 years."
After leaving Old Trafford following the arrival of David Moyes, Meulensteen spent 16 days as head coach of Russian side Anzhi Makhachkala before owner Suleyman Kerimov gutted the playing and coaching staff.