A 1.5M bid has been placed for the Scottish international but it is believed that Championship side Wolves have turned down the offer to let go of their prized asset.
Miller though his currently unhappy at Molineux and is keen to leave, whilst Blades boss Neil Warnock has already mentioned that two or three players have already begun talks with the club.
Wolves chief executive Jez Moxey told wolves.co.uk; "We have received a bid of £1.5m from Sheffield United but Kenny told us he was not interested in a move to Bramall Lane."
"We told Sheffield United that we would consider their bid, although it was unlikely to be accepted, but before we started negotiating we agreed we'd ask Kenny for his thoughts - he said no and so the matter went no further."
Meanwhile unsettled Garry Flitcroft could be heading out of the Ewood Park door. The Premiership Defender has dropped down Mark Hughes pecking order and could leave has plan 3 goes into operation in Lancashire with the Blades top tipped to land Flitcroft first.
Also the latest on the Cameron Jerome sager is that United are about to offer 1.5M to land the striker though could go as far as 2.0M if required.