Gunners boss Wenger may be forced to entertain bids for Theo Walcott before the transfer window closes on Friday night after the club failed to convince the winger to sign a new contract.
Press Association Sport understands Walcott snubbed a deal worth around £4million a year and could now be sold in the next 48 hours for the right price.
Wenger will hold a press conference on Thursday afternoon to preview Sunday's Barclays Premier League game with Liverpool, but the agenda is likely to be dominated by Walcott's future and the implications of allowing another big name to walk away.
It is understood Walcott did not back down over his contract demands but gave assurances he definitely wanted to stay with the Gunners in the long-term.
Walcott reportedly wants to continue negotiations over what is said to be a £75,000-a-week, five-year contract tabled to replace the one that expires next summer.
It is understood the 23-year-old is after a better deal - nearer £100,000-a-week according to reports - and should he and Arsenal fail to reach a quick agreement, it could signal the end of his six-and-a-half-year stay in north London.
Arsenal had been braced for the prospect of selling Walcott before the transfer window closes on Friday but they are now happy to continue negotiations beyond then and effectively risk losing him for nothing next summer.
That is a scenario the club have not been prepared to tolerate in the past, having decided to sell a host of big name players in recent years as they have entered the final year of their contract.
The difference with Walcott is that there is genuine hope an agreement can be reached, although how Arsenal and manager Wenger would react to a big-money bid in the next 48 hours remains to be seen.
Walcott has been valued between £12million and £15million and has already been linked with Liverpool this summer.
Reports suggest Premier League champions Manchester City are also interested in adding the England star to their ever-increasing arsenal of former Gunners after seeing a bid for Swansea's Scott Sinclair rejected.
Walcott's loss would be viewed by many as another huge blow to Arsenal, who lost captain Robin van Persie to Manchester United earlier this month.
Alex Song quickly followed by joining Barcelona, who signed Cesc Fabregas from the Gunners last summer, which also saw Gael Clichy and Samir Nasri move to City.
Walcott was one of Van Persie's main providers last season as the Dutchman notched 37 goals, with Walcott himself scoring 11.
He has often been criticised for a lack of consistency and at both club and international level, and Arsenal team-mate Alex Oxlade-Chamberlain was preferred by England manager Roy Hodgson at this summer's European Championship.
Walcott, who joined the Gunners from Southampton as a 16-year-old in 2006, started their home game with Sunderland on the opening day of the season but was left on the bench for Sunday's match at Stoke, eventually coming on after 72 minutes in what was their second straight goalless draw.
Wenger will be challenged over the club's lack of goals on Thursday, especially from his summer signings.
One of them, Olivier Giroud, has denied he is feeling the pressure of helping fill the shoes of Van Persie.
"I'm not the kind of person to put negative pressure on my shoulders," the France striker told Arsenal Player.
"It's true that Robin had a very, very good season last year but I'm not here to make everyone forget about him or to replace him.
"I only want to take my place, gradually make my mark and win over the hearts of the fans.
"In our way, we are two different players. He spent eight years here and had a very good season last year.
"I need a little adjustment time but I hope to make my mark as quickly as possible. And I hope to score a lot of goals."
Giroud, who signed for Arsenal after a prolific campaign with Montpellier, claimed playing in front of fellow new boy Santi Cazorla would help him adapt.
"It's the same gameplan that we had at Montpellier and the same plan I played with in the French national team, with a number 10 like Cazorla behind me," he said.
"It's the same tactical plan I am used to so I am not lost, I know how to play in relation to my partners and it's just a little adjustment that is needed to make things automatic on the pitch."