The Red Devils had been given a deadline of August 10 as Dortmund were returning for pre-season training today.
They have travelled to Switzerland to begin their training camp ahead of the 2020/21 season, and Sancho flew with the squad too.
United have ultimately failed to reach an agreement over a fee with Bundesliga giants Dortmund, despite ex-Manchester City youth Sancho being ready to make the move to Old Trafford.
As a result, Zorc has said: “We plan with Jadon Sancho. He’ll play for us next season. The decision is final. I think that answers all of the questions.”
Zorc also confirmed that Dortmund will not be issuing Sancho with a new contract.
He added: “We have already extended his contract one year ago until June 2023.
"Last summer we adjusted the salary to the performance development of Jadon. In this context, we have extended the contract until 2023."
Ole Gunnar Solskjaer now faces the prospect of turning his attention elsewhere this summer to strengthen his team in attack.
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The Red Devils have not been prepared to meet Dortmund's £108m valuation of Sancho, especially in the wake of the coronavirus pandemic.
The financial impacts of the Covid-19 crisis have been damaging, even for a club as big as United.
As a result, Ed Woodward did not come to an understanding over a fee, and Sancho now looks destined to stay in Germany at least for this summer.
The window does not actually shut, though, until October, which will likely see United fans hold out hope of a sudden U-turn, even after the Premier League season gets underway.
The 2020/21 campaign for England's top flight is due to start from September 12, although United may not return on that date if they progress in the Europa League.
Their quarter-final tie against Copenhagen takes place tonight in Germany (8pm).