Deegan has been out since sustaining a fractured jaw in early October following the win over Dundee.
Captain James McPake is also in contention following a back injury which has kept the defender out since November 3.
Hibs boss Pat Fenlon said: "If there's hopefully no reaction to the training sessions this week then both of them will come back into the squad.
"They're big players for us in terms of their character and their ability, but also on the pitch in relation to leadership."
Following last weekend's 3-0 loss at Inverness, Fenlon could opt to bring back McPake and Deegan from the start.
Defender Tim Clancy is also nearing a return following a groin injury.
"Tim is maybe a week, 10 days away," Fenlon added.
"It's important to have them all fit coming into this period when we have a lot of games coming up."