A 5-0 thrashing at home to Liverpool has led to calls for Solskjaer to be sacked by disgruntled supporters - many of whom left the Theatre of Dreams at half-time of the record defeat to their rivals.
It has been a poor run of results for the Red Devils, losing three of their last four Premier League games, while they had to come back from 2-0 down to beat Atalanta in the Champions League last week.
Solskjaer labelled the Old Trafford loss 'the darkest' of his career as United boss but vowed to keep fighting on, despite the greater scrutiny he finds himself under.
Former Liverpool midfielder Danny Murphy was scathing about Solskjaer and the performance United put in and doubts whether the manager can come back from such a crushing defeat.
"You have a personal pride and have to get yourself going, but the manager dictates the way the players play and the tempo and attitude you show," Murphy told White and Jordan on talkSPORT.
"The way you train and conduct yourself, all of it comes from above.
"As we've said on many occasions, the repercussions for bad performances aren't there and haven't been there for quite a while.
"The physical stats are damning. The numbers now we can see where United are bottom of table in defensive play, you can't hide from that.
"I don't see how he can turn it around. It has gone too far the other way."
Replacements for Solskjaer are already being talked about with Antonio Conte and Zinedine Zidane among the frontrunners.
Both are currently without jobs and could be parachuted in at Old Trafford.
Conte has Premier League experience having guided Chelsea to the Premier League title during his time at Stamford Bridge.
European football expert Andy Brassell believes both elite coaches would improve things at Old Trafford, but argues that Conte might not be best suited to the task of coming in halfway through a campaign.
He told talkSPORT: "I still find it difficult to imagine him taking over at United mid-season. The idea that he can't do a salvage operation I don't think is correct.
"You look at how he took over Juventus, who were placed seventh. This is going back to the start of Juventus' recently placed dynasty.
"He gave players the speech on the first day saying 'aren't you fed up with being so rubbish'.
"You can imagine him giving a similar speech to the Manchester United players.
"Midway through a season? I'm not really sure. I think that's a difficult ask for him.
"He's a demanding guy with very specific demands."
Zidane does not have the previous Premier League experience, but he has worked with Cristiano Ronaldo before and countless other top name players, and has a glittering record of four Champions League titles and two LaLiga crowns in his two spells as Real Madrid manager.
Brassell added: "Zidane is another interesting one because he has been parachuted in mid-season before. That was his first season at Real Madrid.
"What speaks for Zidane more than anything else, yes he was part of Real Madrid and was coach of Castilla, was assistant to Ancelotti in 2015 and those are very important things and no way of replicating those things.
"He is someone who gets through to star players."