The 20-year-old, who is also attracting the interest of Tony Mowbray's Hibernian in Scotland, finished last season on loan with League One outfit Barnsley.
It is thought that the Hartlepool-born player (pictured) would prefer joining David Hodgson's side for the coming season, as it is closer to his North East home.
Murphy is one of several players Hodgson has been running the rule over, as he looks to bolster his Quakers squad.
Portuguese duo Joaquim Ferraz Vitor Viera and former Raith Rovers hit-man Sebastien Ferrero have been showing their abilities to the Darlington manager while the Stockport County duo of Michael Byrne and Rob Jones will have another chance to impress Hodgson next week.
