The table-topping Gunners have seen strikers Olivier Giroud and Nicklas Bendtner suffer ankle injuries - intensifying speculation that Fulham veteran Dimitar Berbatov will switch to the Emirates Stadium.
Walcott said of the situation: "To be fair that is for the manager to decide if he wants to go out and buy anyone, whoever will come to the club in January, if not it is going to make the club stronger anyway.
"It is always nice to have competition with players coming in, but January is such a difficult period in the transfer market to get players in, especially the top players.
"The boss has already said that he is looking for special players and we have got a lot of special players in that dressing room."
Arsenal returned to the top of the table, one point ahead of Manchester City, after a late double salvo secured a 2-0 victory over Cardiff at the Emirates Stadium on New Year's Day.
On the chances of the Gunners maintaining their challenge for the title, Walcott added: "If you want to win titles then you have got to go to the end and the thing about this team at the moment is that we never give up.
"Every game that we win the belief gets stronger and stronger."