The reigning A-League premiers have approached the 38-year-old Swedish superstar's agent Mino Raiola about a guest player deal, which would reportedly see him play up to six games for them.
Ibrahimovic's contract at LA Galaxy, who were beaten 5-3 by local rivals Los Angeles FC in the MLS Cup Western Conference semi-final last week, is set to expire at the end of the year.
He has scored 30 goals in 29 matches this season for Galaxy, earning a place in the MLS Best XI for 2019.
"We just sent an email to his agent" Perth chief executive Tony Pignata told SBS Italian.
"We learned that his contract with LA Galaxy will expire at the end of November. We made an inquity to see if he wants to come here for a couple of months, for four of six games as a guest player", he said.
It is in fact rumored that Ibrahimovic might seek a move back to Europe during the next transfer window which opens on 1 January.
If successful, signing Ibrahimovic would constitute one of the biggest marketing coups in A-League history.
The former Malmo, Ajax, Juventus, Inter, Barcelona, AC Milan, Paris Saint-Germain and Manchester United forward has also been linked with South American teams Boca Juniors and Flamengo.
