Manager Arsene Wenger wants a quick resolution to the Van Persie saga so he can either prepare for the new season with the Dutchman in his plans or have enough time to find a replacement.
Wish you were here? Arsenal target Fernando Llorente and his girlfriend on holiday in Ibiza
And Sportsmail understands Wenger and his scouting team have spoken at depth about a move for Spain forward Llorente should their talisman leave.
The 27-year-old - who scored 28 goals for Bilbao last season - has a ?28million release clause written into his contract.
And Wenger would use the ?20m-plus from Van Persie's sale in his attempt to lure the striker.
At 6ft 5ins, Wenger believes Llorente has the physical attributes and ability on the ball to deal with the rigours of English football.
But whether Bilbao would be willing to negotiate a deal below his hefty release clause remains unclear.