Milik no longer has a future at Juventus, with the Polish striker frozen out of the first-team picture even as Italy's transfer window winds down. His path out of Turin, however, may run through the Gulf rather than anywhere in Europe.
Several of the leading clubs in the United Arab Emirates have made enquiries over the 31-year-old, a country increasingly viewed in football circles as something of a scaled-down version of Saudi Arabia's spending power.
The Emirati transfer window does not close until 28 September, leaving time to negotiate a deal even at this late stage of the European calendar. Juventus would reportedly be willing to let Milik leave for nothing rather than keep him on their books, with the forward already excluded from Igor Tudor's plans; the only obstacle now is persuading Milik himself to accept a temporary, at least, farewell to European football.
The UAE is far from the only market still trading. Israel and Serbia both close their windows this week, on 16 and 18 September respectively, while several Asian leagues remain open beyond the UAE deadline, including Indonesia (21 September) and Vietnam (30 September).
Japan's window shuts on the same day as Israel's. A number of African leagues have even longer to run, with Morocco and Uganda closing on 16 and 19 September, South Africa and Tunisia on 21 September, the Comoros on 30 September, Libya on 6 October, Ethiopia on 18 October and Senegal as late as 23 October.
In the Americas, Costa Rica, Nicaragua and the Dominican Republic all still have registration windows open through the coming fortnight, closing on 16, 18 and 22 September respectively.
For Milik, whose game time at Juventus has dwindled to almost nothing, any of these markets could in theory offer an escape route. But it is the UAE, with its growing reputation for high-profile arrivals and a deadline that gives all parties breathing room, that appears the most realistic destination if he does decide his future lies outside Europe.