The Dens Park club took the decision to dismiss John Brown earlier this week after falling behind Falkirk at the top of the SPFL Championship table, with Hartley installed as the immediate favourite to take over as his replacement.
The 37-year-old resigned from his position as manager of Alloa Athletic earlier this year and the Recreation Park side might be willing to waive their right to a compensation fee were Hartley to take charge on Tayside. That would make negotiations easier, while his reputation as a coach has been bolstered after leading Alloa to consecutive promotions and into the Championship.
The former Scotland midfielder is now expected to return to the league in the guise of Dundee manager and the club want to have him in place in time for Saturday's match against title rivals Hamilton Academical.
A win then could take Dundee back to the top of the league table - Falkirk are also in action away to Queen of the South - and the challenge of gaining promotion is not expected to faze Hartley.
"They always expect to be up there and I'm sure Paul with deal with that pressure and kick on," said Darren Young, the current Alloa captain and a former Dundee player. "This is a guy who has played at Parkhead for Celtic in front of 60,000 fans and turned in great performances for Scotland. Pressure is something he will shrug off.
"He has played in cup finals and in huge games during his career, and he has taken that experience into management, so I have no fears for him. Paul is definitely ready for that step up."