The 23-year-old had been tipped to join Championship side Crystal Palace after the Eagles had reached an agreement with the Blades for the striker's services over the weekend.
However, Blackman turned down Palace's approach amid speculation that Reading were interested.
The Royals have now firmed up that interest by submitting a bid, according to Sky Sports News.
Blackman is now expected to travel for a medical at the Madejski Stadium, where he will sign a contract until the summer of 2017.
The centre-forward has scored 14 goals in all competitions this season.