The 25-year-old Swedish international has been a mainstay for Rotherham United in the Championship.
However, Rotherham's relegation to League One is likely to mean that Johansson leaves.
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Per The Star, he could be on the move for as little as 1 million if they do go down.
At that price, the Blades would be very eager to bring him into the club in the off-season.
Given they are also up for relegation, Johansson may be back in the Championship next term.