Martin is available on a free transfer after leaving Ipswich earlier this summer.
The 26-year-old was snapped up Manchester United from Wimbledon before making the move to Ipswich in 2006 after loan spells at Royal Antwerp, Rangers, Stoke City, Plymouth, Sheffield United and Nottingham Forest.
Martin made 37 appearances for Ipswich last season, but he was allowed to leave when his contract expired.
A number of clubs are thought to be keen on Martin, but Millwall are hoping to win the race for the skilful wide-man.
Millwall boss Steve Lomas is keen to bolster his attacking options ahead of the new season and is hoping to lure Martin to the Den.