The attacking midfielder, aged 20, has featured in Rovers’ last three pre-season games and once again caught the eye in Saturday’s 1-0 win over Huddersfield Town.
Hurst, who has one year left on his Blues contract, is understood to be available for loan or a permanent transfer.
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"It’s just whether the figures work and what we can do,” McSheffrey said on the possibility of a deal.
“He’s done himself no harm because I think with the team we have and started with (against Huddersfield) we have not really got a ball-carrier.
"I thought he did really well when he came on.”
Hurst joined Birmingham from MK Dons but has never made a first-team appearance.
He has played regularly for their under-23 side in Premier League 2 Division 2 – the second highest level of reserve football in England – and spent time on loan at Step 3 side Alvechurch last season.
The club’s chairman, Richard Thorndike, described Hurst as an ‘energetic, creative player’, who can play anywhere across the front free positions.
"He got a couple of assists while he was here and was unlucky not to score,” said Thorndike.
"He’s got good feet, travels well with the ball, and is quite tricky.”
Hurst was recalled by his parent club before sustaining an injury, Thorndike said, which prevented his loan from being extended further.
He added: "Kyle’s a great lad. He’s local to us so I’m maybe a bit biased. I have known him since he left school in the Bromsgrove area.
"I think he will have a career in the game and he will create and score wherever he goes.
"Maybe the Championship is a step too far right now but National League or League Two for the next couple of years will do him good. If you get him on the ball he will hurt the opposition.”
Thorndike has also known new Doncaster signing Josh Andrews since the 6ft 5 striker was nine years old.
"If Josh can get a run of games without being injured he’s a top player,” he said.
"Aerially he’s a joke.
"He’s not refined enough yet for the Championship, but 100 per cent will be.”