The Italy international is on the verge of completing his move to the San Siro giants and will join them for training next week
The Italy international, 23, has long been linked with a move to the Rossoneri and Galliani has made it clear that Poli will join Milan training on Monday ahead of his proposed transfer.
"I had dinner with Poli on Thursday evening and he let me know that he is a big Milan fan. He will undergo his medical on Friday," Galliani told reporters.
"He will be with us on Monday and join the other players in training.
"The move will not be official until Sampdoria have agreed terms with the player moving in the other direction as part of the deal."
Poland international Bartosz Salamon is expected to move in the opposite direction as Sampdoria reportedly acquire 50 per cent of the centre-back's registration.