The 23-year-old forward, who was a reported target of Liverpool and Arsenal last summer, has expressed his wish to leave Palermo.
Hernandez scored 14 goals in 28 league appearances to help the Sicilian outfit gain promotion to Serie A in the 2013-14 campaign.
"We have not received any offers for Abel Hernandez," Zamparini said to Italian radio station Kiss Kiss. "I believe he will remain with us."
Hernandez joined Palermo in 2009 from Penarol and is under contract with the Rosanero outfit until June 2016.
The South American star is currently on holiday in Uruguay after competing with his national team last month in the World Cup in Brazil.
Hernandez expressed earlier this week his wish to move on in an interview with Uruguay newspaper La Republica.
He said: "I still have two years left in my contract with Palermo but I believe the time has come to leave.
"I don't know if I will stay in Italy or go abroad, we shall see.
"For the time being there is nothing concrete and if no important offers arrive then I will be happy to remain and fight for this club."