The 21-year-old was released by new Ipswich boss Roy Keane last month, causing a stir among keen admirers of the now free agent.
And after making his interest clear, Magpies manager Ian McParland made a firm offer for the Irishman, who scored 17 goals while on loan at Darlington, Northampton and Brentford last season.
McParland is now looking to move things on and told the Evening Post: "If Billy wants to join us then I will be delighted but if not, we need to move on because we have a list of targets - not just strikers but for other positions as well.
"I know that a number of clubs are interested in Billy and he will have a lot of talking and thinking to do when he gets back from holiday. But both he and his agent realise we are serious about signing him, and I am encouraged by the fact that he has not dismissed the possibility of joining us.
"I know some of the interested clubs are in higher divisions than us so realistically, it is still a long shot. But hopefully I can get the backing to make a good offer and we can convince him when we meet that Notts County is the club for him."