Burnley had been hoping to capture the 24 year old after he spent last season with Doncaster notching 15 goals in 30 games.
Blackwell said: “Burnley made an acceptable offer but the move didn’t seem quite right to Billy.
“He’s a great lad and playing for the Blades means so much to him but that desire to succeed for his hometown club can be a bit of a burden for him to carry at times because everyone knows he wants to do well here.
“No manager likes to lose good players and if he does decide to stay he can only make our squad stronger in a tough and unrelenting division in which quality and strength in depth count for so much.
