Petkovic: Zarate an 'important' player
Zarate was widely expected to depart in the transfer window, with Ligue 1 clubs Lyon, Marseille and Bordeaux touted as possible destinations.
But Petkovic said he expects Zarate, who spent last season on loan at Inter Milan, to play a vital role this campaign.
"Zarate stayed here in Rome, where he belonged," Petkovic said.
"They were all just speculations, only speculations.
"Zarate was part of our group from the beginning of the season and he's still part of the group.
"He's improving and showing he's growing and I'm sure he will be important for the team."
Lazio, who qualified for the group stages of the Europa League earlier this week, will continue their Serie A campaign at home to Palermo on Sunday.
Petkovic's men beat Atalanta in their first league outing last weekend, while Palermo lost to Napoli.
"It's very important for us to come back to reality and rest both physically and mentally - that's why I left the team free until Saturday before starting to analyse our next opponent," Petkovic said.
"They were defeated by Napoli, but they are a strong opponent with various champions among them and they will be determined to beat us after their opening defeat.
"We are playing at home, we need to respect Palermo, but we need to prove we are the leaders in our stadium."