Coughlan told BBC Radio Shropshire: "So far as coaching, if there's any way I can help this football club out, I would only love to do it."
"I would do anything along the lines of playing and coaching. This is a great football club."
Two of Coughlan's former managers in Steve Cotterill (Notts County) and former Plymouth boss Paul Sturrock have been linked with the vacancy at the Prostar stadium.
"I know Steve Cotterill personally, I've worked with him, I know Paul Sturrock personally, I've worked with him. I've not spoke to either of them regarding the Shrewsbury Town vacancy.
"I would be very surprised if they weren't on the list and weren't being considered."
Source: BBC Sport
Source: BBC Sport