With Doncaster boss Sean O'Driscoll playing down a move to The Blades, Sheffield born Adams has come back in as favourite ahead of the likes of former Coventry City manager Chris Coleman and Gareth Southgate.
The Yorkshire Post have Bill Bratt, the Chairman of Port Vale where Adams is manager, as saying: "We have received an approach and have reluctantly allowed Micky to speak to them.
"Micky is a terrific manager who has been up front and honest with us throughout the process. It's testament to how well he's done at Port Vale that we have now been approached.
"Micky was offered a new contract before this happened - and that is still on the table. "We obviously want him to stay and we know everyone connected with the club feels the same."