The Gunners chief has the support of current Scotland internationals such as Jon Petrie and Chris Paterson to succeed Williams and the Scottish Rugby Union are looking to name the new national coach before the Autumn Test series against New Zealand, Argentina and Samoa in November.
The governing body are currently sifting through applications for the post with chairman Allan Munro, president Andy Irvine, chief executive Gordon McKie and director Brian Kennedy preparing to interview candidates.
However, Hadden insists his focus is solely on the Celtic League opener against Llanelli at Stradey Park.
He said: "I am fully concentrating on the job in hand here at Edinburgh.
"In fact, it has been very easy and straightforward for me to focus on Edinburgh.
"Edinburgh are simply taking up all my energies at the moment and anything else is peripheral."