The Serie A giants posted a tweet on Friday welcoming the arrival of the winger, but it was later deleted and no confirmation over the transfer followed.
Speaking ahead of Milan's key Serie A clash with Napoli on Saturday, Galliani confirmed that talks are ongoing and would not offer any hint as to whether the deal will go through.
"I am authorised to say that the negotiations for Deulofeu are continuing," he told Mediaset Premium.
Asked if Milan were confident that the transfer will be concluded, he replied: "The only thing I can say is that the negotiations continue."
Everton manager Ronald Koeman stated this week that he would not stand in the way of a move for Deulofeu as he was keen to find the best option for the player.