Solskjaer's future at Old Trafford is under the spotlight once again after United slumped to a woeful 5-0 defeat to their arch-rivals at Old Trafford.
Fans and pundits have rounded on the Norwegian with the club insisting they have no immediate plans to part ways with him.
But in the wake of their horrendous performance against Liverpool, speculation is mounting about Solskjaer's longevity in the job.
According to SkyBet, former Real Madrid boss Zinedine Zidane, Leicester's Brendan Rodgers and ex-Chelsea chief Antiono Conte are among the frontrunners to replace Solskjaer should he be shown the door.
The likes of Mauricio Pochettino, Erik ten Hag and Laurent Blanc are also in the mix according to the bookies.
Here's the list of top contenders in full, according to SkyBet.
Zinedine Zidane 3/1
Brendan Rodgers 7/2
Antonio Conte 9/2
Mauricio Pochettino 10/1
Erik ten Hag 16/1
Laurent Blanc 16/1
Julen Lopetegui 20/1
Julian Nagelsmann 20/1
Gareth Southgate 25/1
Joachim Low 25/1
Massimiliano Allegri 25/1
Ralf Rangnick 25/1
Roberto Mancini 25/1
Solskjaer believes he still has the backing of the club's hierarchy despite the humiliating 5-0 loss at the hands of Liverpool.
Asked if he believes he still has that backing from above, Solskjaer said: "Well, I've heard nothing else (on my future) and I'm still thinking about tomorrow's work.
"Of course, we're all low. I can't say now that I've felt any worse than this. This is the worst I've been, the lowest I've been but, as I've said, I accept the responsibility and that is mine today and it's mine going forward.
"Today's rock bottom, low in confidence but next week it's Tottenham away, it's a Champions League game at Atalanta, the next team who visits us… that's Man City.
"We have to look forward, we have to sort the frames of mind out and make sure we go into the next training session and the next game with the right frame of mind."