The Sun reports that United boss Sir Alex Ferguson is hoping to complete a £22million deal before the Premier League starts this weekend.
Van Persie is desperate for a move to Old Trafford to be completed.
Arsenal were demanding £25million for the striker, but are now prepared to settle for less.
Van Persie scored 37 goals in all competitions for Arsenal last season.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.