The Netherlands international has only made one Serie A appearance since September and has long been linked with a move away from San Siro.
Milan CEO Adriano Galliani confirmed to Mediaset Premium late on Sunday that a deal for the 31-year-old could be completed before the transfer window closes, though he ruled out bringing in any reinforcements.
READ MORE | Mihajlovic job safer after derby win
"There are ongoing negotiations with LA Galaxy for De Jong but things will only be concluded when the contracts are exchanged," he explained.
When asked if Milan would make any late signings, Galliani added: "No, absolutely not. If we look at the number of players in the squad, we're covered numerically in every department."
Striker Luiz Adriano saw a transfer to China collapse in January but Galliani would not rule out further negotiations over the Brazilian, with the Super League transfer deadline not until later in February.
"At the moment there is nothing new. The market in China is open until February 26 but I don't know," he added.