United are understood to have had their offer rejected with Manchester City and Juventus also in the hunt.
Ferguson confirms Manchester United bid for Robin van Persie
It is understood that 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 (Dh85.5m) but Arsenal are thought to be demanding in excess of £20m for their star player.
The Gunners are said to be prepared to hold out for more than £25m 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.
Last season's Premier League top scorer would join them on their pre-season Asia tour, although Arsenal were keen to stress his non-involvement was due to the striker having only trained for four days since returning from holiday..
Arsenal have already signed two new strikers in Lukas Podolski and Olivier Giroud but are also said to be lining up Athletic Bilbao's Fernando Llorente were Van Persie to leave.
Elsewhere, Swansea City signed Spanish midfielder Michu from Rayo Vallecano for £2m as new manager Michael Laudrup continued to rebuild his squad.
Michu, 26, full name Miguel Perez Cuesta, agreed a three-year contract and joins defender Chico Flores and midfielder Jonathan de Guzman as new arrivals.