Aamir, 22, whose five-year ban for spot fixing ends in September this year, is already playing domestic cricket with the special permission of the ICC.
A source close to the player said that a top former Australian player had got in touch with Aamir's manager recently.
"The manager was told that apparently the Melbourne team was interested in having Aamir play for them in the Big Bash this winter," the source said.
The source made it clear that while Aamir was interested in the offer nothing was final as yet.
Aamir, who is currently playing in the national super eights T20 event in Faisalabad for Rawalpindi and has bowled impressively, had said that his main priority was making a comeback to international cricket.