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It had been reported earlier in the day that United, Manchester City and Juventus had all made offers for the Dutch forward.
And Ferguson, speaking to MUTV on the eve of a pre-season encounter with Ajax Cape Town in South Africa on Saturday, confirmed there had been contact with the Gunners.
"Obviously Arsenal have given out the fact that we've made a bid for him," said Ferguson.
"We try to keep business as close as possible to us until the moment we conclude a deal. There's no point talking about something that might not happen.
"There are other clubs interested in the player. We've shown an interest and that's where we're at at the moment."
Ferguson refused to expand on those comments in a press conference.
"We try and do business before we announce anything," he said.
"That is what we are going to do. There is nothing more to add."
The qualities of van Persie, who was named Player of the Year both by the media and his fellow professionals in recognition of his phenomenal 36-goal contribution for Arsenal last season, are obvious, but United's most pressing needs do not appear to be in attack.
With England duo Wayne Rooney and Danny Welbeck at his disposal already, in addition to Javier Hernandez, Ashley Young, new-boy Shinji Kagawa, plus, for now, Dimitar Berbatov, Ferguson seems to have plenty of firepower.
However, midfield is the area where United looked short last season.
Despite Ferguson's assertion, Arsenal have not in fact made a public statement regarding any bids they may have received for van Persie, but would certainly stand to benefit from starting a bidding war for the player.
United, City and Juve are said to be happy to pay somewhere in the region of £15million but Arsenal are thought to be demanding in excess of £20million.
The Gunners are said to be prepared to hold out for more than £25million for the Dutchman, who has confirmed he will not sign an extension to his contract, which expires in the summer.
It was learnt on Friday afternoon that van Persie would not travel to Asia on Saturday on Arsenal's pre-season tour, though the Gunners were keen to stress his non-involvement was due to the striker having only trained for four days since returning from holiday.
A formal announcement regarding van Persie's inclusion is not expected until Saturday, before they fly out.
The van Persie saga is shaping up to be a carbon copy of those that saw Cesc Fabregas and Samir Nasri both sold last summer, something which dragged on towards the tail end of the transfer window.
United lost out to their neighbours' superior spending power in the battle to sign Nasri and it will presumably require something other than pure finance for the Old Trafford outfit to snare their man this year.
Arsenal have already signed two new strikers in Lukas Podolski and Olivier Giroud but are also said to be lining up Spain star Fernando Llorente were van Persie to leave.
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