The 31-year-old has been told he has no future at Dingwall by boss Derek Adams and has been made available for loan.
Adams has already offloaded striker Steven Craig to the Ton's Irn-Bru First Division title rivals Partick Thistle this month and, having added former Hibernian winger Ivan Sproule and German forward Steffen Wohlfarth to his squad in recent weeks, has informed McMenamin he is free to leave the Highlands.
The striker has just four months left on his County contract, and his capture would be a timely boost to Moore, whose side are currently five points clear at the top of the First Division table.
With Archie Campbell still sidelined through injury, the Greenock gaffer has relied on veteran duo Peter MacDonald and Peter Weatherson in recent weeks to keep their promotion bid on track.
Campbell enjoyed a superb start to the season but has struggled for fitness recently and has not featured for a month due to a pelvic injury.
The 22-year-old has still not returned to training with the Ton squad and Moore admits inactivity is the only way forward.
He said: "It is a really unfortunate injury for Archie to pick up and the only cure is rest."