The club have begun negotiations with Herrera's representatives over a new contract, with his current deal set to expire at the end of the season.
However, ESPNreport that the 29-year-old has also started to listen to offers from Spain and Italy.
Herrera would be able to sign a pre-contract agreement with a foreign club in January and move at the end of the season for free.
Although Herrera prefers to stay at Old Trafford, the lack of assurances over playing time has opened his ears to other options.
A return to Athletic Bilbao has been mooted for Herrera. He spent three seasons in Basque Country before joining United in 2014.