The Gunners are resigned to losing their forward with his contract expiring next summer.
Sanchez has no intention of signing a new deal at the Emirates.
And that leaves the door open to clubs making a move in the New Year.
The 28-year-old can sign a pre-contract with a foreign club from January.
While he almost joined Manchester City on deadline day for £60m, PSG and Bayern Munich remain keen.
And according to Spanish outlet Don Balon, Bundesliga side Dortmund are now a surprise contender.
Following the summer sale of Ousmane Dembele to Barcelona, Dortmund want a new star player in their ranks.
Pierre-Emerick Aubameyang could leave the Westfalenstadion in 2018 too, so versatile Sanchez would certainly help fill the void in their attack.
Don Balon add the Arsenal ace has offers on the table from City, PSG and Bayern at this stage.
But Dortmund have identified Sanchez as a key target and are looking to pounce.
However, it is said the Chile international will not leave Arsenal for a club that does not lift trophies.
Ex-Barcelona winger Sanchez wants to win more titles.
And with this likely to be the last big move of his career, Dortmund may miss out.
City, PSG and Bayern are all considered giants of Europe capable of competing in the Champions League and for domestic silverware.
Dortmund are not on their level, although it appears that will not deter them from pursuing Sanchez.
They could even look to buy the Arsenal man in January, having earned around £96m from the sale of Dembele.
