The 20-year old midfielder has been sidelined since July 2011 with ankle and knee injuries but is back in the swing of things with the Gunners although manager Arsene Wenger is not getting too carried away.
"We are so pleased that Jack is back in full training. It's been 14 months and that's a long time for someone at his age. It's an eternity, but it's great news," the Frenchman told the club's official website.
"We have to give him a few training sessions to see how he copes and responds to it. That's the delicate, sensitive stage - to choose when to bring him in and out.
"We'll have to handle that day-by-day."