Bresciano trained with Heart to maintain his fitness during a four-month ban from club football over transfer irregularities earlier this season.
The 34-year-old returned to action with Al Gharafa and has earned a place in Ange Postecoglou's Socceroos squad for the World Cup.
Heart, with owners Manchester City writing the checks, are looking for new domestic and international marquee players, with David Williams now being paid under the salary cap and Orlando Engelaar moving on after his one-season stay.
Speaking to Goal Australia ahead of his departure for Brazil, 73-cap Australia international Bresciano admitted he has received an approach from John van 't Schip's side.
"Honestly? There has," he said when asked if contact had been made.
"But I still have one more year in Qatar with Al Gharafa. And I would want to probably go back there and finish my contract there. The things that happened, I want to stay loyal to them. They did help me through the bad situations and this is my way to thank them. Just to go back there and finish the season with them."
With City's super-rich United Arab Emirates backing, Heart could potentially be able to pay a transfer fee to Al Gharafa for Bresciano's services, a rarity for A-League clubs.
But even if the Qatari club agree to release one of their prized assets, the man himself hasn't decided if he wants to become the face of what could be the rebranded 'Melbourne City'.
"I haven't gone that far to think of that," he said.
"Honestly I haven't thought that far into it. I'll think about it if it does happen."
Bresciano is deeply grateful to his club for standing by him after being sidelined for such a long period, but feels the lengthy break could yet prove invaluable in enabling him to contribute to Australia's campaign in Brazil.
"Obviously that came as a surprise to both my club and myself," he said.
"It was shattering. The first thing that came to my head was the national team, the World Cup. Because I knew how close it was, I knew the duration of the suspension. How that was going to effect my opportunity to make the World Cup (squad).
"In saying that, I had my four-month break, I had the full support of my club. They told me do whatever you have to do to make sure you keep fit, keep match fit. They also allowed me to come back to Australia, train with Melbourne Heart. I'm grateful to both of them, my club and Melbourne Heart, to give me that opportunity to keep my fitness up.
"When the time did come to play my first game after my suspension (ended) I felt good."
"I've seen that this could be a blessing in disguise because I've come in to camp where I'm not burnt out, I'm not mentally stressed or not mentally fatigued."
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This article was originally published at: http://www.footballaustralia.com.au/article/bresciano-confirms-melbourne-heart-approach/19769lvaeboe31h6obt7g16x9d.