His ex-Manchester United team-mate Tomas Kosczak says the Norwegian needs “more time”.
The 48-year-old is under tremendous pressure as his side have not won in four Premier League games.
United also lost 5-0 at home For his fierce rival, Liverpool, in his last league match, where Mohamed Salah scored a hat-trick.
Despite a poor start to the season, former team-mate Koczak believes Solskjaer should be given more time as legendary manager Sir Alex Ferguson did when he first took charge at United.
Kuszczak, speaking exclusively to Ladbrokes, said: “Sir Alex has achieved a lot of great things at this football club, but he only did it because he had the time.
“There were some bad years, and then there were some great years. I hope Ole gets the same opportunity; for now, for me, it’s doing well.”
Kuszczak says Solskjaer “did so much for the team” that people can’t see him.
The former United goalkeeper added: “I know people will argue and say that he had enough time and that the club had not won anything in two years.
JOIN SUN VEGAS: Get a FREE £10 Bonus with 100s of Games to Play No Deposit Required (Terms and conditions apply)
“But he did so much more for the team than we see on the pitch.”
“There is a lot going on behind the scenes that people don’t know.
“To build something within a football team that can last over a long period of time, you have to give you time.”
If Solskjaer gets sacked, Antonio Conte, the winning coach in Italy’s Serie A and Premier League, is one of the candidates to take over.
The Italian is said to be open to the prospect of returning to England and managing a top team again.
However, he will need significant support from the board of directors and want complete freedom in how his team is formed.
The Red Devils have a chance to put Liverpool’s result in the back of their minds when they face Tottenham on Saturday.
Tottenham manager Nuno Espirito Santo is under similar pressure, as he continues to struggle to pull a tune out of his squad.
In an effort to get a reaction from some of his fringe stars, Nuno invited them to “go so far” to fight their way back into the competition.
He said: “I hope all the players are equally committed. But it would be ridiculous to say that this is the reality because the players have their own expectations.
“A lot of them work really hard during the week. Then the weekend comes and the coach decides to go with other players.
“It’s not because you’re not committed, but you’re upset. You’re upset. That’s respectful. It’s not about the commitment of these players.
“These players then have to go further. They have to make a conscious effort that he has to come back again from the start of the week to change the manager’s mindset.
“That’s how it works. In this industry, that’s what a player has to do. Unfortunately, that’s not always the case.”
⚽ Read Manchester United live blog For the latest news and gossip transfers from Old Trafford