Swedish outlet Sportsbladet reported on Friday Gustavsson has already met with the Swedish Football Association and is one of three candidates for the role vacated by Janne Andersson.
The job opened up after Sweden failed to qualify for next year's Euros.
Gustavsson, who is Swedish, is contracted until after Paris 2024, but was also previously heavily linked to the United States women's head coach role since taken up by Chelsea coach Emma Hayes.
In a statement released by Football Australia, Gustavsson didn't address the Sweden reports specifically but stressed his commitment to the Matildas.
"I'm passionate about the Matildas and, as I have stated before, I'm fully focused on qualification and participation at the Paris 2024 Olympics," Gustavsson said in a statement.
"Our team's journey towards this goal is my primary focus and commitment."
Australia can seal qualification to Paris with victory over Uzbekistan in a two-legged home-and-away play-off in February 2024.
Gustavsson led the Matildas to fourth place at this year's home World Cup and fourth at the Tokyo Olympics, their best finish at either tournament.
The Swede has consistently reiterated he has "unfinished business" with the Matildas, planning to develop their style of play while calling for more investment in Australian women's football to keep him "motivated".
Football Australia stressed Gustavsson's contracted status and said they "highly value" his contributions to date.
"We are aware of speculation about Tony Gustavsson and the Swedish men's national team," FA said in a statement.
"Football Australia, however, does not comment on speculative reports or our staff's potential future engagements outside their current contracts.
"Regarding the future of Tony's contract post the Paris 2024 Olympics, discussions will be held at an appropriate time in the future, adhering to our standard procedures.
"Football Australia's immediate priority is the strategic preparation to qualify and participate in Paris 2024 Olympics.
"Football Australia aim to approach this and all future competitions with thorough planning and focused execution."
Gustavsson and his coaching staff are due to arrive in Canada on the weekend ahead of friendlies against the reigning Olympic champions on December 2 and 6.
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