The 37-year-old striker has just finished a successful individual campaign with the LA Galaxy, scoring 22 goals in 27 matches, and is now available to join other clubs on loan until the MLS resumes in early March.
But Leonardo revealed Ibrahimovic was set to remain with the Galaxy, who finished just outside the MLS playoff positions in 2018.
"Ibrahimovic? No he won't arrive. He always said that if LA accepted his demands, that he would stay there," Leonardo told Sky Italy.
"He won't be arriving here. It would've been nice but it isn't possible."
Ibrahimovic was one of the driving forces behind Milan's last Scudetto win in 2010-11 - scoring 14 goals and contributing 12 assists.
The following season Milan fell just short of back-to-back titles as Ibrahimovic banged in 28 goals and was league top scorer before securing a move to French giants PSG.
It's shaping to be a busy transfer period for Milan, with Leonardo also revealing the club is in the hunt for Chelsea playmaker Cesc Fabregas.
The Spaniard has been restricted to only 138 Premier League minutes this term as Blues coach Maurizio Sarri continues to select Jorginho as his creative midfielder.
"We are studying the possibilities [regarding Fabregas]. We are evaluating the conditions," Leonardo said.
Milan sit in fourth position in the Serie A table - 17 points behind leaders Juventus.