The Dutchman, who has been doing ball work for several weeks, returned to the club's London Colney training base towards the end of March.
Boss Arsene Wenger said then that he looked "very sharp" and the striker is now on the verge of being able to resume full training.
Van Persie's return should give Arsenal a timely boost after Tuesday's Champions League exit at the hands of Barcelona, while it is also good news for the Netherlands ahead of this summer's World Cup in South Africa.
Before he was injured, while playing for the Netherlands against Italy, Van Persie had scored seven goals in 11 Premier League games for Arsenal, and his tally of seven means he remains their joint third-highest scorer in the league this season.
Despite his absence the club have maintained a title push and they are three points behind leaders Manchester United with five games remaining, against Tottenham, Wigan, Manchester City, Blackburn and Fulham.
Cesc is doing well, 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 physio Colin Lewin
Defender Djourou has been out since early September with a knee cartilage problem picked up on international duty with Switzerland, while Gibbs broke a metatarsal in Arsenal's Champions League group game against Standard Liege in November.
"Johan Djourou had a difficult problem with the cartilage in his knee joint. 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," said Lewin.
"They have both made full recoveries from what could have been career-threatening injuries."
Gunners captain Fabregas saw his season ended by a broken leg suffered when he was felled by Carles Puyol during the Champions League quarter-final first leg against Barcelona on 31 March.
The Spain midfielder suffered heavy bruising to the same spot on his right leg after a challenge by Craig Gardner in Arsenal's 1-1 draw at Birmingham the previous Saturday.
Manager Wenger has already dismissed suggestions that Fabregas's leg was broken by that tackle, and Lewin also strenuously denied the rumour.
Aaron will make a full recovery - other footballers have suffered a similar injury, the surgery went very well and the early signs are very good
Lewin on Aaron Ramsey
"Cesc is doing well. 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," said Lewin.
"The injury was certainly as a result of the tackle by Carles Puyol at the end of the Barcelona game. There were some ill-informed media reports that the fracture was sustained before the Barcelona game and those reports, put simply, were untrue.
"He suffered heavy bruising in the Birmingham City game but to suggest that someone can run around for 85 minutes against Barcelona with a fractured fibula is just farcical."
There was also good news for Aaron Ramsey, Arsenal's 19-year-old Wales international who bright the tibia and fibula in his right leg during February's 3-1 victory at Stoke.
"Aaron will make a full recovery," Lewin added. "Other footballers have suffered a similar injury. The surgery went very well and the early signs are very good. We don't expect Aaron to return until the early autumn.
"He has some metalwork in there and that provides the stability for the fracture. The specialists have encouraged him to walk and this weight-bearing will aid the fracture healing. It's early days but the signs are very good."
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