United have been heavily linked with a move for the 20-year-old Sancho but media reports say the club have balked at Dortmund's valuation of around 100 million pounds ($131 million).
England captain Kane signed a six-year contract extension with Spurs in 2018 but said in March he could leave if they do not progress in the right direction.
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"Don't get me wrong, Sancho is a top-quality footballer, I think he would improve any team in world football," Scholes, who won 11 Premier League titles with United, told BT Sport.
"His stats say that he is a goalscorer, he will make and score lots of goals. I just think we already have three forwards or wide men that are very similar to Sancho, possibly not quite as good as him, but potentially I think they could be."
Scholes said Kane is the out-and-out goalscorer United need right now.
"I think if that is Harry Kane you are talking about, I would be more desperate to sign him than Sancho at this stage," he added. "I just think United need a centre forward, a real No.9, a real goalscorer, and Kane would be that man for me."

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