The Spanish international is targeting the home meeting with Manchester City on 4th April as a "realistic" date to make his comeback.
He told The Sun: "This week, for the first time since Christmas, I kicked a football. I finally feel like a professional player again.
"If everything goes to plan, I will be back in action for Arsenal in four weeks.
"That will leave me plenty of time to make sure this season is not a complete write-off - for me or for the club.
"Nothing is definite yet, but I've got one eye on the home game against Manchester City on 4th April for my return.
"I genuinely believe I will return fitter and stronger than ever as a result of the first long break of my professional career.
"Maybe the injury was my body's way of telling me to take a break. It's still possible I could play another 15 games for Arsenal this season, but that would involve going all the way in the FA Cup and the UEFA Champions League.
"Everyone at Arsenal has to stay strong. We all have to believe we can still finish in the top four."