The 20-year-old England forward has agreed a new contract extension, which is understood to run until 2013.
Despite the disappointment of another campaign which promised so much but failed to deliver silverware following the midweek Champions League defeat to Manchester United, Walcott maintains there is genuine hope for the future.
Key to Arsenal's success will be retaining the services of men like captain Cesc Fabregas and Dutch international Van Persie, who is the leading scorer this season despite a spell out injured.
Wenger wants the 25-year-old Holland international - who joined the Gunners in May 2004 - to play his part in Arsenal's future.
"I am hoping he will sign a new deal and I am trying very hard to get him to sign. I want Robin on board," said Wenger.
"He is a very important player in the squad and on the pitch he is a very efficient player."
Wenger added: "We want him to stay because we gave him a chance when he was in a very bad position at Feyenoord.
"I think he developed well here and I don't see a reason for him to go and he loves the club.
"We will let you know as soon as we get close."
Wenger maintains the club must do all they can to keep the players they have nurtured.
"You cannot imagine that we work as we did with young players and give them a chance, then let them go," he said.
"We are criticised because we play young players, then we are supposed to let them go when they are in a position where they start to perform at the top level? That is not acceptable."
Walcott, meanwhile, is in no doubt what this group of players can achieve under Wenger, whom he describes as "the best manager in the world".
The Gunners boss insists the best is yet to come from Walcott, who spent some four months out with a shoulder problem earlier this season.
"Theo is an intelligent player with amazing ability and speed, and has developed extremely well this season," said Wenger.
"Theo has huge potential for the forthcoming years and we are all looking forward to see him grow even more in an Arsenal shirt."
Wenger declared: "Theo is 20, so of course the best starts now."
Walcott joined Arsenal from Southampton in January 2006 and has since gone on to become a regular for both club and country, netting a famous hat-trick for England in the World Cup qualifier against Croatia earlier this season.
The pacey young forward is optimistic of what Arsenal can achieve.
"The likes of Robin and everyone else, it shows the belief I have got in this team because this team can go very far," Walcott said.
"Every time I have a warm down I look around the team and see there are some really good players here and I want to be part of it.
"Hopefully we can be right up there with Manchester United, Chelsea and Liverpool and have a great challenge for it next year."
Walcott added: "We have got loads of big games coming up. Hopefully we can get that third position, we have still got to believe in that.
"But I am definitely ready for next season, next season is going to be a big year for me and the club and I am ready for it.
"The main thing is to win trophies and I think this club can definitely win them."