The Gers have been extremely busy during the opening weeks of the January transfer window, securing loan deals for both Jamie Murphy and Sean Goss, while they also managed to make Declan John's loan move permanent shortly before the window opened.
The 32-year-old has been a peripheral figure at Carrow Road this season, making just five appearances in the Championship, but will undoubtedly bring a significant amount of experience with him if he does indeed arrive in the Scottish Premiership.
The defender has made more than 300 appearances for the Canaries since arriving in 2009 and has collected 29 caps for Scotland, so Graeme Murty perhaps feels that Martin will help to make the defensive unit slightly more solid.
If he does get his deal across the line, Martin could be in line to make his debut for the Gers when they take on Fraserburgh in the Scottish Cup next Sunday, while his league debut could come three days later when they face Aberdeen.
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