The England international will see his current deal at Emirates Stadium expire at the end of the season.
With no extension agreed as yet, there is a fear that Walcott will become the latest high-profile figure to sever ties with the Gunners.
Talk of a move in January has also been touted, with Arsenal reluctant to lose him for nothing if a parting of ways becomes the only option.
Arsene Wenger has, however, attempted to play down such reports, with there a desire on his part to strike a deal, and Walcott has offered no indication that he is edging towards the exits.
He told Arsenal's official matchday programme for their UEFA Champions League clash with Montpellier on Wednesday: "I am leaving it all to my agents and you will be the first to hear when something happens.
"It's important for me that something gets sorted out, because I enjoy playing for this club.
"I don't think you can put a timeframe on when it will be resolved, though. When both parties are sure, it will happen when it happens.
"My last contract took six or seven months, so we have to be patient, myself as well. But I'm enjoying my football at the moment, so it's not affecting me at all on the pitch."