Toivonen is currently with Ligue 1 side Toulouse but has yet to make an appearance for the side this season and local fan website lesviolets.com says he is now a target for Victory.
He previously played for Rennes but featured in the Premier League during a brief loan spell with Sunderland in 2015.
The centre-forward scored at Russia 2018 for Sweden and also served up an assist in his five World Cup appearances.
Swansea were circling the star for a loan deal earlier this week, but now Victory - still looking to replace Besart Berisha after his move to Japan - are also said to be in the mix.
The 6'3" striker has 64 caps for Sweden, scoring 14 goals, but has also played for Malmo and PSV Eindhoven before ending up on the bench for Toulouse.
Swedish football journalist Kent Jonsson added: “In my opinion Toivonen can do a little bit of everything.
"He can play as a striker up front or a second striker, or they could use him in a No. 10 role.
"He is not bad in the air and has a mean streak, which could be very useful.”