Madine was released from prison in Leeds yesterday after serving just four months of an 18-month sentence for a double nightclub assault.
Sheffield Wednesday could sack the striker, who had been training with former club Carlisle before his sentencing.
"If Sheffield Wednesday decide he's not their cup of tea and he doesn't have a club, I would be interested without a shadow of a doubt," Kavanagh told the News & Star.
"I have been in touch with Gaz and we have sent each other letters to keep his spirits up. I was hoping to visit him with his uncle, but couldn't find a suitable time.
"I think he has an issue with Sheffield Wednesday. They suspended his contract depending on what they were going to do.
"He has been out of football for a long while so it will take him a while to get back up to pace."
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