Heart this week flagged the likely arrival of an 'international striker' to the club, and rumours quickly emerged suggesting Mifsud was the player in question.
Club chief executive Scott Munn has told SBS Heart have 'agreed terms' with Mifsud.
In something of a contradiction to his comments on the potential transfer, Munn went on to say: "But until we finalise a deal and sign a contract we are not prepared to make any public statements."
He later tweeted: "Just to be clear. We have not agreed or signed anything."
Heart opted not to hand a contract to Brent McGrath following the Australian centre-forward's trial period with the club, and Munn acknowledged their interest in Mifsud is driven - at least in part - by his potential commercial impact.
"We hope to get this deal over the line because his presence would boost our home gates for sure because there are many Maltese living in Melbourne," Munn said.
"He is a hero among the Maltese."
Apart from his exploits with his national team, Mifsud is best known for scoring the goal which helped Coventry City knock Manchester United out of the League Cup in 2007.
The 32-year-old is a free agent, having left Valletta in his native Malta at the end of last season.
