The three clubs are all understood to have all declared their interest in buying want-away striker van Persie but have so far failed to meet the Gunners' valuation of the 28-year-old.
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 for their star player.
The Gunners are said to be prepared to hold out for more than £25million for Van Persie, 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.
They will announce on Friday afternoon whether last season's Premier League top scorer will join them on their pre-season Asia tour, which they leave for on Saturday.
According to widespread reports, manager Arsene Wenger will opt against including van Persie, who this month went public with his desire to quit the club.
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.
City and Juve have long been linked with Van Persie but the apparent interest from United is something more recent and could spark a bidding war for his services.
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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