Despite the fact that he has impressed during three consecutive starts in recent weeks after a long spell out of favor, Walcott has still yet to agree to extend his contract beyond next summer.
Liverpool have long been suggested as a possible destination for the England international, however Wenger has again insisted that Walcott will not be sold in January.
The Arsenal boss did concede that time is running out to reach an agreement, with Walcott able to negotiate a pre-contract agreement with overseas clubs from January.
"We continue in a positive way. I told you many times we have until the end of December to sort this out," he said, according to ESPN.
If Walcott does leave then Sterling will likely be seen by many as an ideal replacement. The 17-year-old has made a big impression this season, commanding a regular place in the Liverpool first team and making his England debut in last week’s friendly with Sweden.
Although there have been various reports of negotiations breaking down over a new contract for the Jamaican-born winger, Liverpool boss Brendan Rodgers has spoken of his confidence that Sterling will remain at Anfield.
“Raheem is in a really good place here,” he said, according to the Daily Telegraph. “He has been given an opportunity here this season.
"He will tie himself down to a new contract because he wants to be here and he can be a great here.”
Sterling is far from the only big name player to be linked to the Gunners in recent days with the Daily Star reporting that Wenger has put Schalke midfielder Lewis Holtby at the top of his wanted list. Arsenal have regularly been linked with the Germany international, who has an English father, in recent times.
With the 22-year-old’s contract set to expire next summer, his future is sure to remain a hot speculation topic for the foreseeable future.
The Star claims that Wenger will pursue a move in the January transfer window when he will likely be available at a knockdown price. However, the story also claims that Liverpool remain interested, while in the past Everton have also been mentioned as possible suitors.
Arsenal could also go head-to-head with Liverpool over Wigan goalkeeper Ali Al-Habsi, according to the Daily Mirror. There has been regular speculation in recent weeks that Wenger is unhappy with the goalkeeping options at his disposal and will look to strengthen in January.
While Liverpool’s Pepe Reina has been mentioned as a target, the Mirror claims that Wenger has been tracking Al-Habsi, 30, since last season. Al-Habsi is believed to be valued at £7 million by Wigan, a price that Arsenal may be reluctant to pay for a player of his age and who, perhaps, would not be a guaranteed starter.