Gunners forward Walcott has been ruled out for the remainder of the season after rupturing the anterior cruciate ligament in his left knee during the 2-0 FA Cup victory over Tottenham on Saturday.
Wenger does have the option of playing Serge Gnabry on the wing, while Alex Oxlade-Chamberlain is also now close to a return from his lengthy injury lay-off, but the Frenchman may yet be forced to add to his squad this month.
“Walcott’s injury has accelerated speculation first and of course my desire as well – but let’s not forget about Serge Gnabry who can play in the first team,” Wenger told the club’s official website.
“We have Oxlade-Chamberlain back and we have many other players who can play on the flanks so to find better solutions than what we have internally will not be easy.
“Up front we lose Theo as a potential central forward and that’s maybe where we have to look outside.
“But we hopefully have Bendtner back in three weeks. We are there for the opportunities but it’s very difficult at the moment.”
England international Walcott will miss the World Cup in Brazil this summer as a result of his injury but Wenger believes the 24-year-old has the character to cope with his long absence.
“Theo is handling it as well as you can when you have had such a shock because he’s mentally strong, he’s very balanced as a person and he can put it into perspective,” Wenger said.
“We know that he will have the dedication and the serious attitude to come back as strong as ever.
“We lost a very talented player, a very intelligent player and a player who was just grabbing his form again.
“From game to game he became more influential, you’ve seen a complete player.
“He can always decide a game through a final ball or through a goal. Sometimes in the same game he does both.
“I felt against Tottenham he had a very convincing performance because he integrates well our style of play as he’s been here for so many years now.
“When we combine at a high pace he’s involved in it because he understands exactly what we want to do.”
Walcott will obviously be absent for Monday’s Premier League game against Aston Villa but Oxlade-Chamberlain’s return from a knee injury will provide a welcome lift for Wenger.
The Frenchman added: “It is unbelievable because he played the first game of the season, against Aston Villa, and now he is back and available and it is against Aston Villa again.
“That makes it five months where has been completely out, so that means he is fresh and that should give us a boost.”
Olivier Giroud and Mesut Ozil could also feature against Villa, while Aaron Ramsey, Kieran Gibbs and Thomas Vermaelen all have an outside chance of being in the squad.