Woodward will leave Old Trafford at the end of the year, much to the joy of many United supporters.
The announcement came as the European Super League proposals folded.
Sancho has long been a target for the Red Devils, but Woodward never came close to Borussia Dortmund's valuation.
Woodward believed Dortmund's deadline date was nothing more than a negotiation tactic.
This impacted the relationship between the two clubs, but with Woodward gone, the Daily Star reports United feel they have a better chance of signing Sancho.
The 21-year-old is out of contract in 2023, and if they fail to qualify for the Champions League, Dortmund could be tempted into selling one of their prized assets.