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Solskjaer is growing under increasing pressure following a string of poor results.
The Red Devils have already been beaten by Crystal Palace and West Ham in the Premier League, scraped a 1-0 win against minnows Astana in the Europa League and had to rely on penalties to beat Rochdale in the Carabao Cup.
Former United defender Parker feels his old club have enough problems and that sacking Solskjaer would only make things worse.
He told talkSPORT: “I just think it doesn’t make sense for Manchester United to sack a manager, whether you want to call it a sacking or leaving by mutual consent. I don’t think they can at the moment because they’ve got enough issues going on.
“I think they are in such a bad place at the moment it would throw more mud at the club if they were to get rid of Ole.