The lifelong Dee fan is open to the idea of a move back to his home town.
However, as yet, player and club have been unable to reach an agreement.
Negotiations are set to continue over the coming days, with both parties hopeful of thrashing out a deal.
The capture of Adam (34) would mark a significant tooling-up of Dundee’s squad ahead of what promises to be a highly competitive, curtailed Championship season.
The Dark Blues kick off their quest for promotion away to title-rivals Hearts on October 17.
Should Adam put pen to paper, he will become their fourth summer signing, joining Lee Ashcroft, Danny Mullen and Alex Jakubiak in committing to the Dens cause.
