Tottenham’s star defender is wanted by the Portuguese as a solution at left-back.
Mourinho has publicly called for more investment in the transfer market from United.
And for the January window, a left-back is said to be high on the manager’s agenda.
Rose, 27, has been strongly linked with United this season and could be available for around £50m.
According to the Mirror, though, Mourinho is being left frustrated by Woodward suggesting younger and cheaper alternatives.
United’s executive vice-chairman is said to have told the boss that players must be offloaded if he wants Rose.