The 32-year-old Australian was released by Turkish club Galatasaray at the end of last season and has been involved in negotiations with at least two A-League clubs, while also being touted to teams across Europe.
Victory had been reported in local media as having given the Sydney-born striker an ultimatum and, when that passed, posted a statement on the club's website.
"In relation to media reports surrounding the deadline, Melbourne Victory Football Club can confirm that it is in the final stages of discussions with Harry Kewell and his management," read a statement
"We expect to be in a position to announce an outcome shortly."
Securing the services of a player regarded as one of Australia's finest exports would be a major coup for Victory, the twice A-League champions who boast the largest crowds in the league.
Kewell has spent his entire senior career in Europe after going to England as a 15 year old for a trial with Leeds United.
Having been pilloried in the Australian media for his financial demands, including a cut of the gate for away matches, Kewell was given an extra incentive to find a club when he was left out of the Australia team to play Wales in a friendly next week.
Coach Holger Osieck said the 54-cap international was "not in very good shape" but hoped he would be fit again for Australia's opening World Cup qualifier campaign against Thailand in Brisbane on September 2.
