Forward Alexis Sanchez has been left out of Arsenal’s Premier League match at Bournemouth on Sunday.
The 29-year-old is out of contract in the summer and has been linked with a January move to Manchester City.
However, City are unwilling to match the Gunners’ £35m asking price and rivals Manchester United are understood to be keen to sign him.
Manchester United boss Jose Mourinho said Sanchez is a “phenomenal player” on Friday.
He added: “What we believe is there are some players in the football world, if you have the chance to sign them in January, March or July, you have to try. And that’s it.”
Liverpool and Paris St-Germain have also been linked with Sanchez, but the player’s preference is to join City.
“Normally he would stay until the end of the season – but we’ll see,” said Wenger on Friday.
“Nothing is really concrete at the moment and nothing is decided one way or another. Of course, I want a quick resolution.”
It is understood Arsenal’s hierarchy have accepted that Sanchez is likely to depart after three and a half years at Emirates Stadium.
However, the Gunners are reluctant to sell without replacing the Chile international and their first choice is Bordeaux’s 20-year-old Brazilian forward Malcom.
If a deal cannot be agreed with any club, Sanchez will be able to leave when his contract expires in the summer – a situation Arsenal are keen to avoid as they would receive nothing.
Sanchez almost joined City for about £60m on the final day of the summer window, only for the transfer to collapse when Arsenal failed to sign Monaco and France midfielder Thomas Lemar.
|Sanchez’s time at Arsenal|
|July 2014 – joins Arsenal for £35m from Barcelona on a four-year deal, despite interest from Liverpool and Juventus|
|May 2015 – finishes the season as Arsenal’s top scorer with 25 goals, including a goal in the FA Cup final win over Aston Villa|
|May 2016 – finishes season with 17 goals, despite missing over a month with a hamstring injury, but the Gunners fail to win a trophy|
|May 2017 – top scores for Arsenal again, with 30, as they win the FA Cup but fail to qualify for the Champions League|
|August 2017 – agrees a £55m move to Manchester City, but Arsenal cancel the deal when they fail to sign Thomas Lemar to replace him|
|January 2018 – after the forward scores eight goals in the first half of the season, City again consider signing him with six months left on his deal|