It has been reported that United, Manchester City and Juventus have 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
"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
However, midfield is the area where United looked short last season.
Despite Ferguson's assertion, Arsenal has not in fact made a public statement regarding any bids it 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 £15 million ($22.6 million) but Arsenal is thought to be demanding in excess of £20 million ($30.2 million).
The Gunners are said to be prepared to hold out for more than £25 million ($37.7 million) for the Dutchman, who has confirmed he will not sign an extension to his contract, which expires mid-2013.
Press Association Sport had learned that Van Persie would not travel to
The Van Persie saga is shaping up to be a carbon copy of those that saw
United lost out to its neighbour's 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 its man this year.
Arsenal has already signed two new strikers in
English Premier League
French defender Gael Clichy has signed a new four-year deal at Manchester City.