The Dutch international has missed five months of action with an ankle injury sustained in Holland's friendly with Italy in November, but has returned to light training this week.
Manager Arsene Wenger has expressed optimism that he will be able to call upon the striker for the final few games of the season, and Van Persie is cautiously optimistic about his chances.
"I am medically fit, but physically I have to gain," he told Dutch television programme Studio Voetbal.
"Only then can I train with the full group. I'm not there yet but I've left a difficult period behind. For a few weeks I've been training with the ball and it looks good.
"I still hope I can take part in the final phase of the league and hopefully the Champions League. This has been my goal from the beginning.
"My first goal is to play for Arsenal. When I said that a few months ago, I looked crazy.
"But as it stands now, that will happen. Only then can I think about the World Cup."
After defeating West Ham United at the weekend, Arsenal are second in the table and firmly in the Premier League title hunt.
Prior to his injury, Van Persie was in fine form for the Gunners, netting eight goals in the 15 games he appeared in.
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