Kenny has been suspended by the Blades pending a Football Association enquiry after the banned substance ephedrine was found in his system in May, but Blackwell has placed his trust in Ian Bennett and Justin Haber.
Blackwell said: "Until Paddy's immediate future is decided I can't make a decision, but competition here is already fierce.
"Benno has been round the block and knows the score, while Justin has improved no end and he must compete with Ian for consideration.
"Whatever happens, my first-team goalkeeper has to be the best in the club, so it is going to be an interesting season for Justin in which to show what he can do."
Kenny, 31, is understood to have told Blades officials he had taken a cold remedy, which contains ephedrine, during the two-legged play-off semi-final with Preston at the end of last season.