Zarate spent last term on loan at Inter Milan.
The player's agent Luis Ruzzi, told Lalaziosiamonoi.it: "We spoke with the Dynamo president about 10 days ago.
"Mauro was immediately left fascinated by their project. We are talking about a permanent transfer.
"The boy is happy, he's married to the cause and there are no other alternatives for him - it's either Lazio or Dynamo."