The midfielder, along with Heath Hocking (calf), Jason Winderlich (soreness), and Tayte Pears (rest) are all in line for a recall to face the Hawks, while midfielder Ben Howlett could return after being omitted last week.
Zaharakis missed Saturday's win over Greater Western Sydney after scans revealed a minor fracture in his back.
His inclusion would add strength to an Essendon midfield still without captain Jobe Watson. After a week's rest the club is hopeful Zaharakis will be available.
"He's going to train this week and he'll be pushing up for selection," Essendon football operations manager Steve Alessio told AFL.com.au.
"From all reports he's pulled up really well from the break and he's a real chance this week.
"The injury didn't affect the way he can train and run. Obviously we'll put him through his paces in the main session on Tuesday and if he comes up all right we'd expect him to play."
Hocking has not played since the Bombers' round-12 win over Gold Coast, but has trained in the past week and is set to return.
"He's another one we'd be very hopeful of coming back," Alessio said.
Winderlich's injury history was taken into account last week when he sat out the Giants game off a six-day break.
The 28-year-old has played 11 games this year and was best afield in round 16, but coach James Hird has previously signalled Winderlich would take managed rests through the rest of his career to prevent injury.
"For him, because of his history, he's one we're going to be more cautionary with," Alessio said.
Essendon is into its most successful season in a decade, having not won 13 home and away games in a year since 2003.
The Bombers' premiership credentials will be tested against the Hawks, with the club confident it can improve further.
"To be where we are at this time of the year is always encouraging. We know we're not quite there yet with the brand of football we want to play," Alessio said.
"So for us we want to continue to improve right throughout this season, right through to the last round and potentially deep into finals.
"We've got to make sure we don't drop off with the way we want to play, and what better team to test that against than Hawthorn."
Callum Twomey is a reporter for the AFL website. Follow him on Twitter at @AFL_CalTwomey
