Pressure was growing ever further on the current incumbent on Wednesday evening as Atalanta raced into a two goal lead in the Champions League clash at Old Trafford.
A stirring second half comeback, complete with obligatory Cristiano Ronaldo winner, did something to make Solskjaer’s position a little bit more secure.
But ask the bookies and he’s still odds on to leave his current job between now and Christmas, as short as 4/11 to exit the club by the end of the Premier League season.
With that, attention is naturally turning to who could be next up for the Old Trafford hotseat and Carnlough man Rodgers is the current fancied favourite, priced as low as 2/1* - in from 5/1 last week.
The Leicester City boss did speak about his future as recently as last week, when he was being linked with the now vacant managerial job at Newcastle United.
And his quotes, including that he is “100 per cent” committed to Leicester, would indicate that he has little intention of abruptly upping sticks like he did at Celtic when the Foxes came calling.
“I’ve got a contract until 2025. I absolutely love being here,” he said.
“I’m very fortunate, I’ve got a great chief executive (Susan Whelan) who runs the club, a director of football (Jon Rudkin) I have a close relationship with and a group of players I really enjoy working with. We have an infrastructure here that allows us to compete.
“For me, as long as they don’t want to move me, I’m very happy here.”
Of course, that “very happy” could perhaps be tested if a club of the global stature of United were to come calling. It would be a remarkable appointment if it were to come to pass, given Rodgers’ history as Liverpool boss between 2012 and 2015.
He would be the first manager ever to take charge of both the north east rivals.
But if not him, then who?
The bookies’ frontrunners also include PSG boss Mauricio Pochettino (7/2), former Chelsea and Inter Milan chief Antonio Conte (6/1) and two-time Real Madrid manager Zinedine Zidane (15/2).
Cristiano Ronaldo is available at 16/1 ahead of England’s Gareth Southgate at 20/1 and both Graham Potter and Leeds chief Marcelo Bielsa at 25/1.
If you want a really outside bet, you can get John Terry and Neil Warnock each at 500/1 with Steven Gerrard at 250/1.
*Odds via PaddyPower