The England international is out of contract in the summer and talks are ongoing to find a solution that is acceptable to all parties after he rejected a reported £75,000-a-week offer during the close season.
Wenger has made no secret of his wish to hold onto Walcott and told a Thursday morning press conference: "We are talking.
"It is very difficult to be predictable in these kinds of situations but our desire is there to do it as quickly as possible and ready to do it.
"I only speak for our side, and my side is that we want him to stay here.
"Of course I don't want to speak much more about that situation because it can be misinterpreted and I don't think he is only interested by money. I don't believe that."
Walcott has been in fine form recently, scoring a hat-trick against Newcastle at the weekend to take his tally for the season to 14 and boost his hopes of being played as a central striker more regularly.
The 23-year-old said after that incredible 7-3 victory: "Talks are ongoing and I am sure something will be sorted. I've been saying that I want to play up front and I am showing the manager what I can do.
"I believe I will be a striker and it's about taking the opportunity when I get it."
Meanwhile, veteran French defender Sebastien Squillaci has admitted he is seeking a move away from The Emirates.
The 32-year-old said: "I am experiencing this situation which I am not enjoying. Given offers, I will leave, possibly during the window or else I will wait until June.
"Returning to my native region, PACA (Provence-Alpes-Cote d'Azur), would interest me. Marseille, Nice, Monaco, Ajaccio and Bastia are the clubs who are talking to me. I am 32, I have two or three good seasons left in me."