The Gunners may have already moved to bring in fresh faces Olivier Giroud and Lukas Podolski, but there is still work to be done to convince Van Persie to extend his contract past next summer.
Italian champions Juventus have made their interest clear, while Premier League champions Manchester City are said to be on the verge of putting down a £20 million offer with more than £200,000-per-week wages for the Netherlands striker, who is now away on holiday following a disappointing Euro 2012.
Wenger, though, knows just how important van Persie, 28, is to the club, having netted 37 goals in all competitions last season.
Wenger said: “We want to keep Robin van Persie at all costs, because we depend on him offensively.
“I have always supported him even in the hardest times, and I hope he will end his career at Arsenal.”
Meanwhile Blackburn have made their third signing of the summer, bringing in former Portugal striker Nuno Gomes on a free transfer. Gomes will join midfielder Danny Murphy and striker Leon Best in signing for Rovers.
Elsewhere Grant Holt has agreed a new three-year deal to stay at Norwich.
The 31-year-old striker, who scored 15 goals to help keep the Canaries in the Premier League, handed in a transfer request at the end of last season that was rejected by the club.
The Canaries are reported to have knocked back several bids from newly-promoted West Ham, and following talks with new Norwich manager Chris Hughton, it was yesterday confirmed club captain Holt would remain in Norfolk.
In ScotlandMalcolm Murray, the chairman of newco Rangers, has apologised for the collateral damage caused throughout Scottish football during the crisis at Ibrox.
Murray issued the apology on the day Scottish Football League clubs met to discuss whether Rangers should compete in the Irn-Bru First Division if Scottish Premier League clubs reject their top-flight application today.
Many of the SFL sides believe the newco Rangers should enter the league at the lowest tier as, despite speculation some SPL clubs were considering a change of heart, a place in the top flight looks unlikely.
* Chelsea striker Daniel Sturridge is undergoing tests for suspected meningitis.
The 22-year-old fell ill over the weekend and was admitted to hospital for tests.
Sturridge’s condition is said to have improved, but his place in the Great Britain Olympic squad is clearly in doubt.