The 23-year-old is the latest product of Crewe's famed academy system to draw attention from afar.
Murphy has spent his entire career to date with the Alex, making close to 200 appearances since making his senior bow in 2008.
Wolves believe he would be a useful addition to their ranks as they prepare for life in League One.
They could, however, face competition for his signature from higher up the Football League.
The likes of Swansea, Leeds, Middlesbrough and Blackburn are all believed to have cast admiring glances in Murphy's direction.
Crewe have resigned themselves to the fact that Murphy will be on his way out of the club this summer, and are looking to get the best possible deal.
The terms tabled by Wolves are considered to be acceptable and it now remains to be seen whether a transfer scramble will be sparked.