Manager Andy Hessenthaler said: "We were impressed with his performance in the friendly with Dagenham.
"I've spoken to the chairman and had a chat with the lad and we're going to put something to him."
If terms can be agreed then Martin could go straight into the squad for Saturday's game at Macclesfield.
The Gills need cover at full-back as Callum Kennedy has now returned to Swindon Town following his loan spell.
Martin has not played for anyone else this season so Hessenthaler can sign him outside the transfer window.
The son of Alvin Martin, he played youth football for West Ham and Tottenham before moving to Blackpool in 2008 where he made 25 appearances.
He was released by Ian Holloway as the Tangerines prepared for their first season in the Premier League.