Aston Villa, Derby County and Fulham are the other sides keen on Kane. The 25-year-old is a free agent this summer after being released by the Blues.
Kane impressed on loan at Hull City last season, playing 41 times in all competitions and even scoring three goals.
The Blades are keen on the defender as a potential replacement for George Baldock. Baldock has been strongly linked with a move to Celtic.
The Sheffield Star reports that United have a strong link with Chelsea that dates back to when Chris Wilder first became manager in 2016.
They and Manchester United are believed to be their strongest partners in the loan market. It was what saw Blues goalkeeper Jamal Blackman spend the 2017/18 campaign on loan at Bramall Lane.
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Therefore it is unsurprising they are looking at possible options in West London. However, is Kane the full-back they should be targeting?
The Chelsea player Sheffield United should really want
It would be an ambitious move, but the Blades should really be looking at trying to sign Reece James.
James had a hugely impressive 2018/19 at Wigan Athletic which saw the 19-year-old named in the EFL and PFA Championship teams of the year.
The teenager is tipped for great things, with the Metro claiming Brighton and Hove Albion, Leicester City and Manchester United are all interested in him.
Yet Chelsea understandably want to keep James at Stamford Bridge for the long-term. Which is why Wilder could offer to take the defender on loan next term.
United are preparing for their first season in the Premier League in 12 years. If Baldock were to leave then James would be a more than adequate replacement.
There are problems with a potential deal, however. With the Blues set for a two window transfer ban, it’s thought James may be moved to the first team to act as backup for Cesar Azpilicueta.
The youngster is also currently sidelined for up to three months after damaging ankle ligaments during an England Under-20s game.