The 23-year-old is out of contract in the summer but that has not affected his form for the Gunners after switching to his preferred role as a central striker and grabbing a hat-trick against Newcastle.
Walcott turned down one offer of a new deal - reported to be worth £75,000 a week - in the summer and has so far failed to reach an agreement as the player looks for weekly terms closer to £100,000.
Wenger remains confident a conclusion can be reached to keep hold of a player he helped mould from a raw teenager into an England international.
"It is a positive message for us to keep Theo, of course. Will it have an effect on the morale of the team? Yes, I am convinced it will have a positive effect if we manage to sign him," Wenger said.
Speaking at a press conference this morning ahead of Sunday's FA Cup third-round tie at Swansea, Wenger added: "It is very difficult to be predictable in this kind of situation, but I always said that our desire is there to do it as quickly as possible. We are 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."
Arsenal are expected to move in the transfer market during January, with reports of a £10million bid tabled for Atletico Madrid striker Adrian Lopez.
Wenger said: "Arsenal has a good reputation outside England and many players want to join us, but at the moment all these players are under contract.
"The most important players for us are those who are here. Those who are on the transfer market will not help us win the games.
"So first of all we have to make sure the players who are here stay here, after we look outside.
"Let's first try to finalise with Theo Walcott and after if we need something else we will go somewhere else, but our first priority is that."
Fringe players like Morocco forward Marouane Chamakh, French centre-half Sebastien Squillaci and Swiss defender Johan Djourou - who is said to be interesting German side Hannover - are all likely to be offloaded.
"Squillaci, if he finds a club, he will certainly go. Djourou might go somewhere as well, that will be decided in the next 48 to 72 hours," said the Arsenal manager.
Wenger expects to take a full squad to Swansea, with midfielder Abou Diaby and full-back Andre Santos now back in training after their injury lay-offs.
Reserve goalkeeper Vito Mannone has been suffering from a virus, as has midfielder Emmanuel Frimpong following his return from a month loan at Charlton.
The FA Cup was the last trophy won by Arsenal in 2005.
Wenger, though, maintained talk of Wembley and ending that long drought was not yet on the agenda.
"Swansea is a difficult tie, but of course we want to come out on top of it. For the rest, it's the first round we come in, so people will speculate a lot (about) who will win it in the end," he said.
"(To have) a chance to do that, you just need to get through the first round (you take part in)."