The Birmingham Mail says Malmo have a relatively young squad - their average age is in the region of 23 - so would welcome his experience and could offer Champions League football next season.
However, Rosenberg's salary would be a major sticking issue.
The striker earns more than £30k-a-week at Albion, which would put him out of Malmo's reach as things stand.
Rosenberg has previously said that he would like to play for his home-town club before he retires. He also still has a property in the area.
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