The Argentinian returned to the Biancoceleste last month after a disappointing season-long loan spell at Inter Milan, where he scored just three goals in all competitions.
The 25-year-old has been linked with a move away from Rome this summer.
"Mauro's hope is to remain at Lazio," Zarate's agent Luis Ruzzi to Corriere dello Sport. "He is happy and wants to impress the new coach (Vladimir Petkovic).
"Last year he knew he was not wanted by the previous coach and it was hard for him.
"But he is happy to remain here and play for Lazio. He is under contract.
"Would he be willing to reduce his contract?
"Mauro would be open to that possibility as he turned down quite a bit of money when he joined Inter on loan."
The South American is under contract with Lazio for another two seasons.