The Argentine 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 northern summer.
"Mauro's hope is to remain at Lazio," Zarate's agent
"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.
Italian football turns its attention to Rome on Sunday (Monday AEST) as Roma and Lazio square off in what should be a highly charged Coppa Italia final.