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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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?