Torreira was allowed to join the Italian side on loan from Arsenal last summer as he has no future at the Emirates Stadium under Mikel Arteta.
Fiorentina have an option to make the move permanent for a fee of €15m and the club are keen to hold on to him after a series of committed displays in a purple shirt.
The Uruguayan has impressed in Italy this season and has won the hearts of the Fiorentina fans in the process.
But according to Italian daily Corriere dello Sport, Fiorentina are hoping to get a discount on the fee they agreed with Arsenal.
The Italian giants are keen to renegotiate the fee in order to pay less than they initially agreed with the Gunners.
Fiorentina have money to spend following the sale of Dusan Vlahovic to Juventus in January, but are keen to see whether Arsenal would be prepared to accept less money.
Arsenal may well be unlikely to entertain such requests and are expected to ask Fiorentina to cough up the sum they agreed on last summer.
Torreira is happy at Fiorentina and is keen to stay on at the club beyond the end of the season.
