Motherwell forward Murphy, who is out of contract at the end of the season, has again been linked with a move to Ibrox.
The Gers are currently unable to sign any players due to a 12-month transfer embargo imposed by the SFA for failure to pay taxes. However, they will be able to register free agents from September 1, 2013.
Gers boss Ally McCoist and scout Neil Murray have identified several targets who could boost their threadbare squad next season. And Murphy, who was linked with a move to the club he supported as a boy at the start of last season, is believed to be one of them.
His former team-mate Bob Malcolm believes a move to Rangers would interest the 23-year-old –even though he would be playing in the Second or even the Third Division. The former Gers ace said: "At the start of last season Blackpool were keen to sign Jamie, but he decided to stay at Motherwell.
"But I think to progress his career he now needs to move on. It is inevitable. I know he is a Rangers fan so going to Ibrox is something that would interest him.
"I don't know what Jamie himself is thinking. Maybe he doesn't want to go down to the Second or even the Third Division.
"But a few years ago Rangers bid £1million for Mark Reynolds and Motherwell knocked it back. He eventually moved to Sheffield Wednesday.
"Jamie was at the club when that happened and I think that he will realise that getting the chance to move to Rangers might not come around again."
Malcolm spent nine memorable years at Rangers and believes Murphy, who he played with during a spell at Motherwell in the 2008/09 season, would be a success in Govan.
And he is convinced that having to drop down the leagues would not deter him – as was the case with former Hearts and Scotland Under-21 winger David Templeton back August.
Malcolm said: "The Rangers fans would love Jamie; he is direct, is good in the air and he scores goals as well. He is skilful and very talented.
"He has got all of the attributes you need to be a success at a major club like Rangers and I am sure he'd do well there.
"He has another 10 years at least at the highest level. If he joined Rangers he wouldn't be playing in the lower leagues forever."