The Airdrieonians boss believes it would be the best move for the 19-year-old to aid his development.
Patterson started the 2-1 win over Hibs on Sunday, taking his appearances to 12 for the season.
The recent run in the team is due to James Tavernier’s injury but the club captain has recently signed an extended deal.
If game time is going to be limited for Patterson next season, Murray thinks a Premiership loan move would be ideal.
He told BBC: "We're not talking for Rangers here, but if Rangers want to improve young players so much, and their fans and everybody wants to improve Scottish football, why don't they go give Patterson to Hibs?
"Give him to Hearts, St Mirren and don't ask for any money.
"If you want to progress the player and get him games, there you go. But they won't and I understand why."