James Gandolfini -- Tattoo Shopping Before Death

James Gandolfini was in the market for a mysterious new ink job before his death -- dropping by an L.A. tattoo parlor earlier this month ... and promising to return with a special order.

TMZ has learned Gandolfini visited T-Man Tattoo in Studio City on June 1st -- and the owner (pictured above) tells us, the actor was extremely excited about a new tattoo he was planning.

Gandolfini didn't tell the owner what he wanted to get done -- but said he just moved to the neighborhood, and promised to return later this month for a full tat session.

The owner says Gandolfini was in great spirits during the visit.