The executive vice-chairman is feeling the heat following a woeful campaign at Old Trafford.
United finished sixth in the Premier League and failed to secure Champions League qualification.
Jose Mourinho was sacked as manager in December and replaced with Ole Gunnar Solskjaer.
The former United striker engineered a long winning run to land the job on a permanent basis ahead of schedule.
But the decision proved flawed as United managed to win just two of their last 12 games.
To make matters worse Alexis Sanchez has been a huge flop despite earning £500,000-a-week, while doubts remain about the immediate futures of Paul Pogba, David De Get and Romelu Lukaku.
Solskjaer admits United won’t challenge for the title again next season and the Norwegian faces a huge summer of rebuilding.
Woodward admits the season has fallen well short of expectations – but has vowed to back Solskjaer in the transfer market.
Woodward said: “After a turbulent season, everyone at Manchester United is focussed on building towards the success that this great club expects and our fans deserve.
“Preparations for the new season are underway and the underlying strength of our business will allow us to support the Manager and his team as we look to the future.”