The 59-year-old's takeover of the club has been treated with suspicion in some quarters but the former Scotland international has called for supporters to trust the new owner
Green's company Sevco bought the Ibrox giants' remaining assets following their liquidation and is currently attempting to get the newly-formed club back onto the Scottish football ladder.
Hutchison crossed paths with Green during his time as a player at Sheffield United, where the 59-year-old once served as chief executive, and insists that forging a relationship with fans should be the new Rangers owner's first priority.
"If I was him I'd try and appoint someone that's got an affiliation with Rangers and can be a link between him and the fans," the 41-year-old told reporters.
"If he could try and get that link a little bit closer and the fans can trust him, I think he can do a decent job.
"I'm not so sure what Charles's incentives are but I think it's for the good of Rangers Football Club.
"It's going to be very hard for the Rangers fans to trust him because he's an outsider. He needs to get the fans onside now and appoint someone that can talk to the fans because he's a businessman.
"He's probably not going to be able to talk to the fans the way I could or an ex-Rangers player could."
The Rangers newco have recently had their application to rejoin the SPL denied, after several clubs came out against the proposal.
Scottish Football League clubs will now meet on Tuesday to discuss whether the Glasgow outfit can join the Scottish First Division, though there is a possibility of the club beginning in the third tier.
And Hutchinson lamented the club's descent into turmoil but hailed Green's role in bringing the Ibrox side back from the brink.
"When Charles came in, he actually rescued Rangers. He came in and put his money where his mouth is. At a certain point, they have to trust Charles," he continued.
"As football fans, it's come to the time where Rangers just want whatever decision's going to be made to be made very quickly so they can take it on the chin and get on with it.
"It's a sad situtuation that Rangers are in."