The 24-year-old will be sidelined for at least six months after he ruptured the anterior cruciate ligament in his left knee during Arsenal's FA Cup third-round victory over Tottenham on Saturday.
Goal revealed in December that Wenger sent scouts to watch Atletico Madrid's Diego Costa, with the 25-year-old heading the club's five-man shortlist of strikers who are potential targets during the January transfer window.
“[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 [Alex] 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 [Nicklas] Bendtner back in three weeks.
"We are there for the opportunities but it's very difficult at the moment.”