The winger, who impressed during the Olympics, has revealed that the South Coast club have agreed a fee with Bologna and that he has received an "offer that you cannot refuse".
The fee is believed to be in the region of £12m, similar to the amount Tottenham Hotspur offered when Ramirez rejected the London club.
"Bologna will tell me on Friday if I can move," he told Corriere dello Sport.
"The truth is that I think, yes, this time I am moving. Bologna has reached an agreement with Southampton, and there are only a few details to be found but the agreement in principle is done.
"The English club has reached an agreement with me, it is the classic offer that you cannot refuse for my life as a whole and my family."
Ramirez is reportedly awaiting the nod from Bologna before flying over for a medical.