The 31-year-old is currently with Barcelona, on loan until the end of the season from Juventus.
Davids is out of contract with Juve in the summer and had already stated his intention to leave Stadio Delle Alpi.
Juve allowed Davids to join Barca in January and he has been in inspirational form for the Catalans.
Milan had been interested in bringing Davids back to the Giuseppe Meazza - where he spent two seasons after leaving Ajax in 1996.
He joined Juve in 1998, but now looks set to seal a permanent move to Barca after Milan admitted they would not be signing him.
"The Dutch player won't arrive, he's too expensive," said the Rossoneri's vice president Adriano Galliani.
Galliani confirmed that Milan would be looking to add to their squad in the summer with two great players.
"We will buy two champions for next season," he added.
