The Scottish winger was a revelation during his half-season loan at Rangers from Premier League side Brighton & Hove Albion, scoring five and setting up eight goals in 18 starts for the Gers.
It became evident very early on that keeping him at Ibrox would make the Scottish Premiership side a much more formidable force next season, when better players are added to supplement the team's quality.
The Daily Mail reported in January that Murphy was worth a bargain £1 million to sign permanently, and Allen reveals that discussions are underway over bringing the boyhood Rangers fan to Glasgow soon.
He said: "We'll see, no final decisions have been made. We owe the courtesy to those players and their football clubs to speak with them first.
"But once that decision has been taken and made then you guys will get the nod. Yes, there is an agreement in principle to sign Jamie Murphy."
As far as left wingers go, Murphy is one of the very best in Scotland and what a huge boost it would be for Rangers to sign him permanently.
Still only 28, Murphy, who turns 29 in August, has a good few years left before he declines and what a player new Gers boss Steven Gerrard could have at his disposal.
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