Arsenal's 3-2 win over West Brom ensured they finished above north London rivals Tottenham, taking third spot in the Barclays Premier League.
The success represents a major turnaround in fortunes for Arsenal who were in 17th place in October after losing four of their opening seven games, with some fans calling for Wenger to be sacked.
Wenger said: "Will Champions League football help to keep Van Persie? It makes it easier to attract good players and keep them.
"The intention is to speak with him before he leaves for the Dutch camp (for Euro 2012)."