Alexis Sanchez was the subject of a £60million bid from Manchester City over the summer, but the move broke down on deadline day.
The Chilean is into the final year of his contract, and the Gunners are reluctant to let him leave for nothing.
City are eager to strike a deal, with Pep Guardiola looking to reunite with the 28-year-old, whom he previously worked with at Barcelona.
And according to the Daily Mirror, City want to capture Sanchez for a cut-price fee in January.
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Alexis Sanchez's future could be decided in January
He never goes on the football pitch to lose a football game, never. Sanchez is a winner type
The report suggests his value could plummet to £20m, as he will only have six months left on his contract then.
Sanchez would not be cup-tied for the Champions League, as the Gunners are involved in the Europa League this campaign.
The Mirror also claim the Gunners will wait until January to see how their season is faring before taking a final decision on the player’s future.
Meanwhile, Arsene Wenger isn’t worried Sanchez will lose motivation after Chile failed to qualify for next summer’s World Cup.
Pep Guardiola wants to reunite with Alexis Sanchez
“I have no doubt that he wants to perform,” Wenger said.
“He never goes on the football pitch to lose a football game, never. Sanchez is a winner type.
“You have always to set targets when you’re a football player. When one is gone, you focus on something else.
“Sanchez is 29 at the end of the year, so the next one [World Cup] he will be 33. He expected to go. Certainly a big disappointment for him.
“But I believe to play at the top level is dealing with that kind of disappointment.”