After contacts in recent weeks, an intermediary of the Russian club met Milan chiefs at Casa Milan on Wednesday.
Milan value Uruguay international Laxalt, 27, at €10m and are willing to let him leave.
In an attempt to bring down the price, Lokomotiv want to include attacking star Aleksey Miranchuk.
Miranchuk’s age (24), price and talents are in line with the profile Milan are looking for in new signings.
However, Milan would prefer separate operations and are hoping to sell Laxalt in a straight cash deal.
Milan and Lokomotiv will meet again in nine days to further discuss a deal for Laxalt.