Crystal Palace were linked with the player in each of the last two transfer windows.
A striker for whom Crystal Palace reportedly made contact about signing last month has joined another club.
And he will spend the rest of it on loan to Hellas Verona, with his Milan contract due to expire thereafter.
It remains to be seen whether or not Crystal Palace had remained in pursuit of Borini, having already signed another centre-forward, Cenk Tosun, on loan from Everton this month.
But with speculation that Christian Benteke and Connor Wickham could each depart Selhurst Park ahead of the transfer deadline, it is plausible that another option will be sought to compete with Jordan Ayew and Tosun.
Borini came through the ranks at Crystal Palace's London rivals, Chelsea, and would have counted towards the Eagles' home-grown quota.
The Italian also had spells at Liverpool and Sunderland before joining Milan in 2018.
Crystal Palace fans - which players would you like to see arrive at Selhurst Park this month?
Have something to tell us about this article?