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Dortmund have set an asking price of £80m for Sancho and, as reported by The Independent, there is understood to be confidence that a deal can be done after United's failed pursuit last summer.
Sancho is currently away with the rest of Gareth Southgate's squad at St George's Park, readying himself for Sunday's Group D opener against Croatia and said on Thursday that he is not concerned by talk over his future.
"I don't really look at it," he said. "When I'm during the season, I always focus on myself and the team because that's the most important thing that we can do.
"You know, every time I'm on a pitch I'm always giving my all and obviously to create with what I do on a pitch and that's with goals and assists.
"That's why I really try to do and always work hard for the team. No, I'm cool about it.
Sancho added: "You know, there's always going to be speculation, especially when you do well. It's just how you handle that on the pitch and just keep doing what you're doing.
"If you keep on doing that then I'm sure that won't be a problem because the main thing is my football and that's what I'm focused on at the moment.
"Of course all the boys have a lot of questions, you know," the 21-year-old said.
"I feel like that's with a lot of players because we're all such great young talents and, you know, when you do well - again, like I said - speculation is always going to come around.
"Again, I just tell the boys: ‘Look, I'm just focused on football at the moment' and we just focus on the Euros, step by step."
Sancho has struck up a friendship with Marcus Rashford while away on international duty and said that the United forward has made him feel welcome in the camp.
"He is a nice guy, ever since I came into the England squad he has welcomed and is always speaking to me, making sure I'm alright. I'm happy me and him get on well."