The Manchester Evening News reports that the Cottagers are keen to take the 25-year-old on loan from United when the January transfer window opens.
New Fulham head coach Rene Meulensteen is reportedly an admirer of the player and is keen to be reunited with the Brazilian at Craven Cottage.
Anderson has made just two starts for United this season.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.