The 21 year old was told he has no future at Portman Road by recently Town boss Roy Keane, and is now looking for a new club. Several sides are said to be interested in brining in the Irishman, including Brentford where Clarke spent the end of the season on loan, but Notts County are the first to make a solid offer.
Confirming the offer to the Official Notts County Website, boss Ian McParland said: "Billy is in Ireland at the moment following a family bereavement so we haven't actually had chance to meet up with him, but I have spoken at length with his agent.
"Maybe it's a long-shot that we will get him if Championship clubs are involved but you get nothing if you don't try. I've made a firm offer to Billy's agent and he knows that we are serious about signing him.