The bid believed to be £1m has been accepted by the clubs board and comes hot on the heals of Wolverhampton having a similar bid accepted earlier on in the week.
The prospect of Championship football seems a bigger lure for 23-year-old Murphy who looks set to talk to the Lancashire club over the weekend although Leicester City had tested Crewe with a lower bid.
Rovers who is managed by Gary Bowyer and his number two Terry McPhillips knows all about the Alsager born midfielder who coached Murphy when he was part of the academy set up before he moved to Everton.
With things moving at a pace both teams will be hoping the deal can be sorted ahead of Crewe's trip to Cornwall on Monday where the team look to train and play a game against Truro next Friday night.