Elneny injured his knee in January and had to undergo surgery, which ruled him out for the rest of the current campaign.
Elneny has been recovering well since going under the knife and last week he was able to begin running outside.
The 30-year-old took part in a light session with fitness coach Ricky O’Donoghue and first-team coaches Nico Jover and Carlos Cuesta.
Elneny is aiming to be back fit in time for Arsenal’s pre-season tour to the USA in July and is on course to hit that target.
Despite being out injured, Elneny signed a new contract with the Gunners back in February and it runs until the summer of 2024.
The midfielder is currently the longest-serving player in the Arsenal squad having joined them back in January 2016.
He is a popular member of the squad and, as has been the case with injured players this season, manager Mikel Arteta has kept him close to the group despite his injury.
Elneny has travelled to both home and away games with the squad, visiting the dressing room after matches.
The Egyptian made eight appearances for Arsenal this season, scoring once, before he was struck by injury.