Reports earlier this week claimed the deal was in danger of falling through because of Insua's personal demands.
Fiorentina have agreed an undisclosed fee with Liverpool for the Argentina international as they look to bolster their defensive options.
Liverpool are willing to sell Insua despite their lack of left-back options as Roy Hodgson looks to raise funds for his own signings.
Fiorentina are determined to push through the move and it is believed both parties are now close to completing the transfer.
Insua is expected seal his switch to Italy next week to end his three-year spell at Anfield.