The 20-year-old is one of the most promising talents outside the Premier League and has been linked with a move to the top flight this summer.
After impressing in the Blades' ultimately unsuccessful bid for promotion from the Championship, Naughton is reportedly a target for Aston Villa, Mark Hughes' big-spending City and their neighbours United.
However, Everton tried to pip their top-flight rivals to the right-back's signature after lodging an offer with the Blades.
Toffees manager David Moyes is willing to pay an initial £3.5million for Naughton, with incentives eventually taking the deal to £5million.
Blades boss Kevin Blackwell said last week that he was confident of keeping the youngster over the summer - and his club have rejected Everton's opening offer.