The United boss wants Sancho signed as soon as possible to help integrate into the squad before the Premier League campaign starts on September 12.
The transfer window has been extended until October 5, but United are eager to avoid a drawn out transfer saga.
Solskjaer and co will reportedly look elsewhere if a deal cannot be struck with Dortmund.
Dortmund’s determination to keep Sancho for another season has been well received by their first-team squad.
Midfielder Axel Witsel said: “He stays and we are all happy.
“Last year and the first year when I came he’s one of the most important players offensively for our team.
“This is really good news for us to keep him – at a minimum – one more season.”
Erling Haaland added: “Jadon is a fantastic player, so I am very happy that he is staying. I am sure he will give me some goals – but I will give him some as well.”
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Source Daily Express :: Sport Feed