The Blades announced the signing of Woolford on their official website on Tuesday, with the winger recently letting his Millwall contract expire.
Woolford played under Adkins at Scunthorpe with real success, but bringing in another left-sided player had led to questions over the future of prolific winger Jamie Murphy.
The Yorkshire Evening Post had reported Leeds would demand Murphy as part of any deal to sell Billy Sharp to Sheffield United, but Adkins has insisted Murphy is part of his plans.
He told BBC Radio Sheffield of the Woolford signing: "It doesn't mean anything for Jamie Murphy.
"Jamie Murphy is a Sheffield United Football Club player who can play on the right and play on the left and play up front as can Martyn.
"We're trying to get a group of players to get promotion from League One. I'm certainly not looking to move Jamie Murphy on, and will make that perfectly clear. I've spoken to Jamie on several occasions and its competition for places."
Adkins appears to have made his mind up one way or another that Murphy is going nowhere, and will resist any enquiries for the 25-year-old Scotsman.
As promotion contenders he believes Sheffield United can fulfil any goals Murphy has of moving up a level, and the forward can play a key role.
After signing a new contract only in January, Murphy is unlikely to be pushing for a move any time soon.