Santa Cruz is expected to leave City during the January transfer window but prefers a permanent move away from Eastlands.
"We take into account Santa Cruz's reaction and his desire to make any transfer permanent," Lazio president Claudio Lotito said.
"We are aware of this and consider it a wise decision for him."
Meanwhile, AC Milan coach Massimiliano Allegri has admitted that he would welcome the chance to coach Cruz's fellow City striker Mario Balotelli at some point while conceding that he currently has a wealth of striking options at the San Siro.
Milan have recently signed Antonio Cassano and already had Alexandre Pato, Robinho and Zlatan Ibrahimovic so Allegri has plenty of firepower at his disposal.
"I would willingly coach Balotelli," Allegri said. "But it would be difficult given that we have so many champions in our team."