Solskjaer’s position came under scrutiny after defeats by Arsenal and Istanbul Basaksehir last month, but four wins from five games sees them trail Premier League leaders Tottenham Hotspur by five points with a game in hand, and they need only a point to reach the Champions League knockout stages.
“We recognise there’s more hard work ahead to achieve the consistency needed to win trophies,” Woodward said at a fans forum.
“But we see positive signs on the pitch and the training ground that reinforce our belief in the progress being made by Ole, his coaching team and the players.”
Woodward maintained United had kept their promise by recruiting heavily in the summer transfer window despite the club’s financial situation being impacted by the Covid-19 pandemic.
“We will continue to support Ole with a planned, long-term approach to recruitment, focused on the summer windows,” he added.
Woodward also said the club would not take part in any breakaway European Super League and that he was involved in talks aimed at the “strengthening of existing UEFA club competitions”.
“We believe that any changes to European competition post-2024 must be complementary to thriving domestic leagues,” Woodward, a board member of the European Club Association, said.
“Other domestic leagues feel the same way, reflected in conversation with our counterparts in other clubs and countries.”