Broadcaster Sky Sports News understand that the Blades are to beat fellow Coca-Cola Championship side Coventry City to the signature of Barnett, 24 who is registered with this Saturday's opponents West Bromwich Albion.
He won't play against the Blades this weekend as he is currently on loan at the Ricoh Arena and has made 11 appearances to date, and whilst Sky Blues have requested to turn his short term loan into a permanent deal he could head to S2 instead.
The Blades are searching for a new centre-half following the sale of Matthew Kilgallon to Sunderland last week with Andrew Davies (Stoke City) and Alex Pearce (Reading) also was mentioned in the tabloids recently.
It is believed that the defender is on the transfer market in the region of £1,000,000.