The 22-year-old is recovering from the broken foot he suffered during England's win over Denmark on March 5, and has stepped up his return ahead of Arsenal’s push for fourth place and FA Cup final against Hull City.
|4/6||Arsenal are 4/6 with William Hill to finish in the top four this season|
"The next three weeks will be very important for him. Can he play this season? Yes."
After reaching the FA Cup final on Saturday following a tense penalty shootout victory over holders Wigan, Arsenal will now focus on league duties having been leapfrogged by Everton into fourth place over the weekend.
Up next for Arsene Wenger and his squad is West Ham on Tuesday, and the manager has revealed his injury crisis has deepened following the win at Wembley.
"I can't give you team news because there are so many uncertainties, muscular problems or fatigue.
"[Tomas] Rosicky and [Laurent] Koscielny we will test [on Monday]. I will decide later whether to take a risk with him.
"The main uncertaintities are [Nacho] Monreal, he has a large bruise, [Alex] Oxlade-Chamberlain, who was not even supposed to play on Saturday, [Aaron] Ramsey, who had to come off with muscle tiredness."
A run of seven consecutive victories has seen Everton move into pole position for the final qualification spot for the Champions League, but Wenger believes Arsenal winning their remaining games will see them finish fourth.
He continued: "We want to finish strong now, we have a battle with Everton and of course it's now down to consistency in our final games.
"We want to achieve it and that's simple. We just want to not imagine the consequences of not doing it, what you want is just to focus on doing it.
"That's where I think we have the focus, the quality of the spirit, we have the desire and we are slowly getting our players back so the squad is not depleted any more. It's much more stronger than it was two or three weeks ago.
"The target is of course to win every game. Experience [of finishing in fourth every season] counts, yes of course. But the difference will be the quality that you produce on the pitch and that is down to desire, to be faithful to our game we want to play, and get everybody back into the squad."