It is understood a fee and payment plan has been negotiated for the 21-year-old winger, who has won nine caps for Uruguay and is reported to be commanding a club record fee of ?12million.
Former club Penarol, who own 30% of his registration, are also satisfied by the terms of the agreement, but it is understood cash-strapped Bologna are stalling as they seek to secure a loan against the repayments.
Southampton are determined for the transfer to proceed having beaten off competition from Liverpool and Tottenham for Ramirez, but are looking at other options in case the deal collapses.
Ramirez last week outlined his desire to swap Serie A for St Mary's.
"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," he told Corriere dello Sport.
"But they believe in me in every way, I will be essential and above all, they are going to grow.
"Southampton are a newly promoted team in the English top flight but they will become a big team in years to come."