The former United captain is available after leaving Nottingham Forest as assistant manager.
“Roy Keane is very unique in the way he conducts himself, how forthright he is, and he does understand the United way and he wouldn't mess about," Murphy told talkSPORT.
“There doesn't seem to be anyone under Solskjaer's wing who has that fire and steel, they're all a bit nodding dogs, but I don't know Solskjaer so maybe he has some steel himself.
“My feeling is, the best management teams I worked under, they have to be on the same page and in it together.
“But this is where I'm struggling with the concept.
“United have empowered Solskjaer with the job, so if you then start choosing his staff, you've got a problem.
“You'd be undermining him. If someone comes in who the manager doesn't really want, you've got a problem already.
“If Solskjaer turns around and says, 'I would love Roy Keane with me', then you've got an exciting team.
“But the conversation between them would have to be, 'look Roy; I'd love to have you with me, you can do things I can, but it's my way', and Keane would have to adhere to that."