Mourinho has been fighting for his job in recent weeks but a slight upturn in results has seen him cling on.
They won three games in a row – including a win in Turin against Juventus – before losing the derby to Manchester City on Sunday.
But Woodward does admit United have suffered a ‘mixed’ start to the season following some woeful results.
Manchester United are 12 points behind league leaders and bitter rivals Manchester City and sit in eighth place.
To make matters worse United are also seven points adrift of the top four and a Champions League place for next season.
But Woodward has tried to remain upbeat and insists Mourinho still has the full backing of the club’s board.
United have revealed first quarter revenues of £135m and Woodward said: “On the pitch we remain well positioned in the Champions League.
“And although we have had a mixed start to our domestic campaign, the squad and the manager are fully united in their determination to regain our momentum in the Premier League.”
Woodward also said United have the ‘financial strength’ to get back to contending for the biggest trophies at home and abroad.
United have not won the Premier League title since 2013 and have not made the Champions League semifinals since reaching the final in 2011.
But ahead of the January transfer window, Woodward insists their is cash available to help United get back to the top of world football.
He added: “Our financial strength enables us to continue to attract and retain top players and to invest in our academy, as we look to drive the success on the pitch that the club and our fans expect.
“We remain on track to deliver our record full-year revenue guidance, underpinning our long-term, strategic plan to create sustainable growth across all areas of the club.”
United’s revenue of £135million for what is termed the first quarter of 2019 was down from £143.7million in the same period last year.
Commercial and matchday revenue were down, along with operating profit, with broadcasting revenue – up £2million to £42.8million – the only area showing growth.
It is understood the difference can be attributed largely to the fixture schedule which meant United played two fewer games than in the same period 12 months before.
United brought in £590million in the year ending June 30, 2018, with revenue expected to rise to between £615m and £630m over the coming financial year.
Wages rose £7.1million to £77million while a smaller summer tour resulted in decreased sponsorship revenue but reduced operating expenses of £28.6million, a decrease of £5.9million.