The former Leeds United, Liverpool and Galatasaray man has been linked with a move back home for the past few months but a deal to join the Victory could be off if he doesn't sign by the close of business Thursday.
The two-time A-League champions have told Kewell that they are now keen to complete a deal but will pull their offer if nothing occurs by the given deadline.
"The time has come for us to get some clarity on the matter," a club source told The World Game.
"We need to know what Harry wants to do. If he accepts what we believe is an excellent offer then that's great but if not then we have to be able to move on and look at other options.
"We feel we owe it to our fans and the public in general to bring a conclusion to what has been a long-running situation.
"Our dealings with Harry's manager Bernie Mandic have been very open and forthright from the word go ... now we just need to know where we stand."