The Ireland full-back missed the last two victories over the Ospreys and Munster through injury, and he joins a squad which includes Shane Horgan, who has scored three tries in the last four games.
Commenting on Dempsey and his main injury worries for the Edinburgh encounter, Leinster coach Michael Cheika said: "I'd say the three injury issues we have this week are Brian O'Driscoll, Dempsey and Stephen Knoop.
"Girv has been out doing some running and kicking, so he's looking okay. But we don't want to aggravate that so we'll wait and see how he comes up later in the week.
"We'll assess Brian later (today) and with a bit more intensity on Wednesday to see if he has gotten over the pressure in his foot and in his ankle. If a guy like Brian says that he can't run out when you know that he'd run all day for you, you make the change and see how the assessment goes.
"When players leave grounds on crutches you tend to fear the worst because of the visual, but he has come up pretty well. He trained this morning in the gym so hopefully he'll be a starter.
"The same with Stephen in that we'll see how he gets on with more contact work. We'll be in a position to make some decisions by Wednesday or Thursday."
Man-of-the-match from Leinster's Magners win over Munster, Malcolm O'Kelly, is included in a strong-looking panel which includes fellow Ireland international forwards Leo Cullen, Jamie Heaslip, Bernard Jackman and Shane Jennings who all impressed last Friday, alongside Stan Wright, Ollie Le Roux and Ireland 'A' back rower Stephen Keogh who made his return from injury.
Friday's game looks set to be another sell-out at the RDS with over 17,000 tickets already sold. A limited number of tickets are still available from www.LeinsterRugby.ie.
LEINSTER Squad (v Edinburgh): Backs (12) - Chris Keane, Cillian Willis, Felipe Contepomi, Jonathan Sexton, Christian Warner, Gordon D'Arcy, Brian O'Driscoll, Gary Brown, Luke Fitzgerald, Shane Horgan, Rob Kearney, Girvan Dempsey.
Forwards (14) - Juan Gomez, Cian Healy, Ollie Le Roux, Brian Blaney, Bernard Jackman, Stephen Knoop, Stan Wright, Leo Cullen, Cameron Jowitt, Malcolm O'Kelly, Keith Gleeson, Shane Jennings, Stephen Keogh, Jamie Heaslip.