Solskjaer has been out of work since leaving Old Trafford in November and Nicholas thinks he is an ideal candidate for Sir Alex Ferguson's former club.
"I was thinking about managerial options for my old club and I would love them to go out and make a real statement of intent.
"Why not go and ask the former Manchester United manager if he is interested? He can only say no, but if you don't ask you don't get.
"People might say he has just managed one of the biggest clubs in the world, why would he even consider Aberdeen?"
Solskjaer returned to Molde in October 2015 and remained there until United came calling in December 2018.
Nicholas added: "I know and I get that but if you look at Solskjaer's CV away from United it has been at the likes of Molde and Cardiff.
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