The 18-year-old broke into Leicester’s first team last season, making 21 appearances across all competitions as they were relegated to League One.
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It was widely reported that Man United are interested in signing Page, with Leicester currently demanding a fee of £10 million.
According to The Athletic, Michael Carrick’s side are still looking to get the deal over the line before the end of the window.
Page's cousin, a Man United fan, posted an Instagram story from the directors' box against Ipswich Town on Sunday, although it’s not thought to be related to the transfer.