The 29-year-old was released by Darlington after their relegation from League Two last season.
Dempsey is awaiting offers from clubs in England.
Bohs boss Fenlon offered the Wexford native the chance to train with the Gypsies to keep himself fit and, while Dempsey still hopes to secure a club in the UK, he has not ruled out a move to Bohs, if an offer is made.
"I haven't spoken to Pat Fenlon about contracts or anything like that for now, I just wanted somewhere to train and keep myself fit and Pat was good to let me train with Bohs," Dempsey said.
"I don't know what the money situation is with Bohs and if Pat is in a position to bring in players, I'll just keep training with Bohs and see how things go.
"I am waiting to see what comes up in England as there is a chance of something happening."