The Norwegian may not be in charge at the club much longer. He was already under pressure prior to Liverpool's trip to Old Trafford on Sunday evening.
That pressure only intensified when United fell to a humiliating 5-0 defeat against Jurgen Klopp's side.
Solskjaer is still in the job - for now - but it seems a matter of when and not if he loses his job.
Who are the contenders to replace Solskjaer at the helm? Could Ronaldo replace the 48-year-old?
It seems unlikely that United's legendary forward will become United's next manager.
However, Paddy Power thinks he has a good chance of replacing Solskjaer.
They have given Ronaldo odds of 19/1 to become United's next manager. Those odds make him the seventh favourite.
Paddy Power thinks he is more likely to become United's next boss than the likes of Michael Carrick and Darren Fletcher, both of which are already staff members at United.
View the 24 favourites for the job below...
It would be a huge risk for United to appoint Ronaldo. He has absolutely no experience in management.
But he would command the respect of each and every player. He's certainly gone through it all as a player and won everything there is to win.
His experience as a player could well translate to management.
Tim Sherwood is one pundit who has backed Ronaldo to become United's manager in the future.
Speaking on talkSPORT last month, the former Premier League player said: “We’ve seen him do it on the international stage, most recently at the Euros, barking out orders," he said.
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"That boy will be a manager 100 per cent. I would have a bet on him being Manchester United manager in 18 months.
"Whenever Ronaldo finishes playing I think he will become a manager, it will be an automatic choice.
"He could bring an experienced coach in there with him – someone like Carlos Queiroz – as he’ll know plenty of them, and I can see him being a manager at Man United in the future."
It would a sight to behold if Ronaldo did indeed become United's player-manager.