Keane, who was sacked as manager of English Championship club Ipswich Town in January, was spotted in the crowd at an Asian Champions League fixture in Sydney on Wednesday, fuelling speculation the 39-year-old might be set to meet Victory officials.
Melbourne, two-time champions in Australia's top-flight A-League, sacked their coach Ernie Merrick last month and are one of the few clubs in the competition not reliant on financial assistance from the game's national administrators.
Victory, who have been coached by caretaker Mehmet Durakovic since Merrick's dismissal, drew 1-1 away to Chinese side Tianjin Teda on Tuesday.
Victory declined to provide immediate comment when contacted by Reuters on Thursday.
Local media had earlier quoted a Victory spokesman as saying: "We won't be commenting on speculation regarding the coaching position.
"Suffice to say, we still have a long way to go in the process of appointing a coach."
The comments have done little to quell the frenzy over Keane's Australia visit, with former Australia goalkeeper and television pundit Mark Bosnich tweeting his enthusiasm.
"Roy Keane to Melbourne would b(e) a gr8 coup for Melbourne Victory and the A-League. Watch this space!!!" he said on Twitter.
Despite the A-League's low profile, a possible role for the former Ireland midfielder in Australia's top-flight would not be without precedent.
Trinidad and Tobago striker Dwight Yorke, a team mate of Keane's at Manchester United, played as a marquee signing for Sydney FC, while former England striker Robbie Fowler is weighing up a second season at Perth Glory after one with the now defunct North Queensland Fury.
