Journalists understand United failed to meet the Gunners' valuation of Van Persie, with Manchester City and Juventus having also fallen short.
Ferguson told MUTV: "Obviously Arsenal have given out the fact that we've made a bid for him.
"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."
United, City and Juve are said to be happy to pay somewhere in the region of £15 million but Arsenal are thought to be demanding in excess of £20 million for their star player.
The Gunners are said to be prepared to hold out for more than £25 million for the 28-year-old, who they appear to have all but given up trying to convince to sign a new deal at the Emirates Stadium to replace the one that expires next summer.
City and Juve have long been linked with Van Persie but concrete interest from United is something more recent and could spark a bidding war for his services.
Journalists have also learnt that Van Persie would not travel to Asia on Saturday, although Arsenal 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.