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Fabregas suffered his season-ending injury against Barcelona in the Champions League quarter-final first leg clash at the Emirates last month.
"Cesc is doing well," Lewin told the club's website.
"He is likely to be out for the rest of the season with a hairline crack of his fibula. If everything goes well he will comfortably make the World Cup and we will be constantly monitoring him."
Arsenal have been hit by several injuries this season, but Lewin revealed that forward Robin van Persie is close to a return, along with Johan Djourou and Kieran Gibbs.
"Johan Djourou had a difficult problem with the cartilage in his knee joint," said Lewin.
"He has made virtually a full recovery and we expect him to train fully with the squad within the next fortnight, as will Kieran Gibbs. They have both made full recoveries from what could have been career-threatening injuries.
"Robin will be joining the squad for full training imminently.
That is a big boost for the club and to see Johan and Kieran training with the team in the next fortnight will give everyone a big lift."
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