The Kangaroos confirmed on Friday that Shaw would step away from his role for an indefinite period of time due to personal issues.
Player-manager Liam Pickering believes North Melbourne should test the waters with Clarkson to see if he is willing to return to the club he played 93 games for between 1987-1995.
“I know it won’t happen, but the other option is Alastair (Clarkson),” he said on SEN’s Off The Bench.
“He’s an ex-North Melbourne [player], I don’t think he’d [accept the offer] as he’s contracted [to Hawthorn], but the reality is the Hawks are in a rebuild.
“I could only see it if Hawthorn was also of the view that with the new group coming through, they need a fresh voice, but I don’t think they will.
“I just think it’s worth asking the question, he’s a favourite son of the club and is mates with [several people at North Melbourne].”