The Ibrox club's chief executive said on Wednesday that Rangers should attempt to leave Scottish football if the league reconstruction plans agreed by the three governing bodies are approved. The Scottish Premier League and the Scottish Football League this week agreed in principle to a plan that would merge the organisations in a 12-12-18 structure.
Green has made his dismay clear at the proposals which, if implemented in time for next season, would mean another campaign in Scottish football's bottom tier – in this case an 18-team National League – for Rangers even if they win the Irn-Bru Third Division title this term.
However, Murray – who was part of the Blue Knights group who tried to buy the Ibrox club last summer – is eager for Rangers to become a positive voice in the debate.
"Charles Green has only been in Scotland for less than a year and dealing with administration in Scotland is a frustrating process," he said. "I'm no longer involved, it's a new era at Rangers and it's got off to a good start. If we're using that to try to rebuild bridges within Scottish football, then I think Charles Green and the Rangers board should actually rise above some of the things.
"No-one is more frustrated with what happened last year than me but I think it's now time for us to rise above that and actually provide leadership to the rest of Scottish football. Charles Green is well positioned to do that.
"With regards to leaving Scottish football, that's been discussed for many, many years. I think Charles Green and the Rangers board should be more focused on improving Scottish football from within."
Murray lost his place on the Ibrox board following Craig Whyte's ill-fated takeover, before joining forces with the Blue Knights when the Ibrox club fell into administration. The whole saga has soured Murray's view of how the game is run in this country but he believes Rangers have a part of play in improving it.
"I wouldn't say they've got an obligation but I think they are better suited to trying to improve the game from within than threatening to leave. I'm not quite sure what that really achieves," he said. "[Green] should use his position to try to engineer change."