The Daily Star reports that the Cottagers are keen to bring in Meulensteen as their assistant manager.
Meulensteen was sacked by Anzhi Makhachkala and Fulham boss Martin Jole hopes his fellow Dutchman will join him at Craven Cottage.
Meulensteen spent 12 years working under former Manchester United boss Sir Alex Ferguson at Old Trafford.
Meulensteen's agent Fons van den Brande said: "Clubs in the Middle East are interested in him, but there are also a few clubs in Germany – and one big club in London.
"The London team want him as a coach alongside the manager. He has to make the right decision after his time in Russia."