Moutinho cost £18million when he joined from Porto in 2013.
But according to Portuguese radio RTP, the Ligue 1 outfit are ready to let the player leave, even though he still has three years left on his current deal.
Monaco have already allowed Radamel Falcao to head to Chelsea on loan and Moutinho could now follow the Colombian to England.
But after United landed Bastian Schweinsteiger and Morgan Schneiderlin it is not thought they are in the market for further midfielders.
Porto are said to be keen to bring the player back to Portugal, while Andre Villas-Boas wants to take Moutinho to Zenit Saint Petersburg.
But Jose Mourinho and Arsene Wenger could yet enquire about landing the experienced international as they look to strengthen their squads ahead of the new season.
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