He could be offered a return to the Blades in the New Year as Blackwell braces himself for the departure of Matthew Kilgallon.
Blackwell is keen to make permanent signings when the transfer window reopens and is considering a move for Davies.
"Andrew is someone we might look at," said Blackwell in the Sheffield Star. "I wouldn't rule anything out.
"When he was here he showed tenacity and a passion to play.
"You can spend a couple of million on someone and then realise they've not got that."
Blackwell is also keeping an open mind regarding Mark Bunn's future, with the Blackburn Rovers keeper impressing on loan for the Blades.
"I'm really pleased with Bunny," added Blackwell. "He's done ever so well."
Meanwhile, reports claim Bunn's Blackburn team-mate Elrio van Heerden will undergo a trial at Bramall Lane ahead of a potential January move.
Van Heerden has made just two substitute appearances in the Carling Cup since joining Rovers in the summer and the South African midfielder may be allowed out on loan to acclimatise to English football.