Celtic's Ronny Deila, Aberdeen's Derek McInnes, Inverness' John Hughes and Hearts' Robbie Neilson are the nominated managers but Strachan feels Neil deserves to be on the list for his first half of the campaign with Hamilton.
Strachan said: "Alex has been tremendous, absolutely tremendous, and should be pleased with himself. He has to be really pleased with what he has done and he seems to be at clubs where you get good support. That's what you need.
"You don't need the support when you are doing well. The best test of a chairman is when you are not doing so well.
"Trophies can't be the only thing. It's about the expectations of the club that you go to and whether you can fulfil them. It's good if you can."
Neil has led the Canaries to the Championship play-offs by winning 14 of 21 games since he took over the Carrow Road duties in January.