The duo are currently with the Brazil squad as they prepare to take on Paraguay in midweek, leaving little time to make it to Liverpool for Saturday’s clash.
With their last outing for the Selecao this month set to kick off at 1.45am (BST) on Wednesday, they are then set for a dash back to Merseyside.
According to the Guardian, Fenway Sports Group have chartered a jet to fly Coutinho and Firmino to Liverpool directly after the final whistle in Sao Paulo.
This should see them arrive back on English soil on Wednesday afternoon, and they could return to training at Melwood on Thursday.
They would still then only have two days before the derby, which is a 12.30pm kickoff, but Jurgen Klopp could opt to name both in his starting lineup in pursuit of victory.
Last international break, Coutinho played 86 minutes in a 2-0 win away to Peru on November 16, before playing 90 minutes in the 0-0 draw with Southampton on November 19.
The 24-year-old is expected to start against Paraguay at the Corinthians Arena, suggesting a similar situation could unfold.
It had been feared that Firmino would miss Wednesday’s World Cup qualifier, however, with the striker rumoured to have suffered a throat inflammation.
But Brazil manager Tite has since confirmed he is fit to start, with his availability a boost for Klopp as he hopes for his players to return from duty without any issues.
Klopp will have no issues with Sadio Mane this time around, however, with the winger playing the last of Senegal’s clashes for the break on Monday evening, against the Ivory Coast in Paris.
Mane scored a penalty in a 1-1 draw at Charlety Stadium, with the game eventually abandoned due to crowd trouble.
He is likely to be back when training resumes this week, joining his team-mates for what will be vital preparations for a must-win game as the top-four race continues.