Fiorentina will reportedly accept Liverpool's offer of Dirk Kuyt as a down-payment for Peruvian winger Juan Manuel Vargas.
It is believed that the Serie A side would also demand £12m for Vargas to leave Florence this summer.
The Viola are not sure if Brendan Rodgers would be interested in a deal to take Vargas to Anfield, but are willing to test the water as they step up their pursuit of Kuyt.
The Dutch forward is likely to leave Merseyside this summer after being marginalised under Dalglish last season.
Hamburg have been touted as favourites to secure his signature, with the 32-year-old admitting a move to the Bundesliga would interest him.