United completed a £72.1 million deal to sign the England international from Borussia Dortmund last week.
Sancho wore the number 7 jersey at Dortmund and wanted to wear the same number, made famous at United by the likes of Eric Cantona and David Beckham.
Veteran Edinson Cavani would have had to give up the number to appease Sancho.
According to MailOnline, Solskjaer vetoed the request and Sancho has subsequently taken number 25.
Speaking about Sancho's signing after the loss to QPR on Saturday, Solskjaer said: "It's a big statement.
"We've followed him for a long, long time. He's a forward with creativity, flair and individual skills. He's got years ahead of him.
"It shows the fans we mean business. We've got one of the best forwards in England for the next ten, 12 years.
"We've got Marcus [Rashford] who's 23 and Mason [Greenwood] who's a young lad so we've got an English core there. The forward line is looking really good."
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