Walcott???s current deal only has one year left to run but talks about an extension are due to resume between his representatives and Arsenal later this summer.
However, while he seems confident a new contract will be in place ahead of next season, Walcott also warned that it may take a while for the deal to be finalised.
The 26-year-old was speaking at an open-top bus parade around the streets of Highbury held to celebrate Arsenal???s 4-0 FA Cup final victory over Aston Villa on Saturday.
Walcott impressed in the final, scoring the opening goal just before half-time, and will now join up with the England squad.
Asked by Sky Sports News HQ if he thought an Arsenal extension was in the offing, Walcott said: ???I am sure things will get resolved. I just want to enjoy today.
“I have got England coming up and then we can think about that process, but it will take time, I am sure.”
Despite the wet weather, thousands of Arsenal fans came onto the streets to cheer the squad and Walcott says they now need to be rewarded with a title challenge from the Gunners.
???It has been a great success this year,??? said Walcott. ???It has been a step up, to finish third (in the Premier League) and win the FA Cup in consecutive years. We want more and more of this.
“These players have the trust in each other and this has got to be a stepping stone now to challenge for the title, because this is what all of these fans dream of.
“We need to do it for them, they have waited a long time.”