Per the source, Depay is in talks with Everton over a loan move to the Toffees over the winter break.
Depay has played just 20 minutes of Premier League football under the stewardship of Mourinho this season and is reported to be keen on a temporary move over the second half of the season to gain more playing time.
Fenerbahce are currently lacking in depth on the flanks with no replacements for Jeremain Lens and Volkan Sen should they pick up an injury.
The Istanbul giants recently beat United 2-1 at the Sukru Saracoglu stadium in the Europa League but Depay did not feature in the squad.
Depay has worked with current Fenerbahce head coach Dick Advocaat in the past during his time at PSV.