Fiorentina have made an increased offer for Diego Rossi of €8m plus bonuses, while LAFC are asking for €12m, claim Sky Sport Italia.
The 21-year-old Uruguayan can play on the left, right or centre of a trident attack.
He would be able to sign on as an EU player, as he also holds an Italian passport.
Rossi left Penarol to join Los Angeles FC in January 2018 and so far in 2019 has scored 14 goals in 27 games between MLS and the US Open Cup.
According to Sky Sport Italia, the Viola sent over a formal offer worth €8m plus performance-related bonuses.
The LAFC asking price is currently €12m, so they are negotiating their way towards a middle ground.