The south-coast side were believed to have agreed a fee with the Serie A club and terms with the player several days ago, but Saints' proposal has since been rejected.
It had looked as though the newly promoted team had pulled off a major coup by landing the highly rated Uruguayan from under the noses of Champions League-chasing sides Liverpool and Tottenham.
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"Bologna didn't want to close the deal without the bank guarantees. I have spoken [on Wednesday] with the English club's chairman and they are looking at another target.
"The player was very happy with the offer received, but now he will probably remain at Bologna."
Betancourt also revealed that it is unlikely that either Liverpool or Tottenham will now return with bids for his client.
"Tottenham is an option to be rejected at this time because they are a long way short of Bologna's demands," he added.
"Liverpool? They have never presented a concrete offer."
The president of Bologna, Albano Guaraldi, had earlier thrown doubt on the proposed moved by stating that Southampton's offer “had not been considered suitable”.