United's sluggish start to the new season has seen talk arise that former Real Madrid coach Zinedine Zidane may replace Mourinho at Old Trafford.
The Manchester Evening News says Woodward is still backing Mourinho to turn things around.
The United vice-executive chairman gave his manager a two-year deal back in March.
And he is reportedly determined to stand by his man despite Zidane's shadow looming over the club.
United chiefs feel their victory over Burnley may be a tipping point.