Brazil play Uruguay in the early hours of October 15, with Liverpool kicking off against Watford less than a day-and-a-half later.
There remain doubts over whether they will be able to feature in the Champions League clash at Atletico Madrid on October 19, too, despite the relaxation of quarantine rules in the UK.
After both started in the 3-1 victory over Venezuela on Friday, the Liverpool duo played a second consecutive 90 minutes each just two days later.
It resulted in a clean sheet for Alisson – his 33rd in 49 games for Brazil – as a 0-0 draw was played out with Colombia in Barranquilla.
Fabinho started alongside Fred in a two-man midfield, with Gabriel Jesus, Neymar and Lucas Paqueta operating behind a sole striker in Flamengo centre-forward Gabigol.
Brazil dominated the game in terms of possession, but neither side was able to craft a genuine opening until the second half – even then, Alisson was busier with efforts from range.
Liverpool’s No. 1 thwarted Mateus Uribe and Juan Fernando Quintero, while the introduction of Leeds winger Raphinha – a long-term Reds target – sparked Brazil into life.
However, neither side were able to find a route through to goal, with a share of the points perhaps a fair result.
Brazil remain top of the CONMEBOL qualifying table after 10 games, six points ahead of second-placed Argentina – who they still need to play – and eight ahead of Ecuador in third with a game in hand.
If Liverpool arrange travel to Madrid ahead of the meeting with Atletico, it would allow Alisson and Fabinho to play in the Champions League, and by returning later than their team-mates they could avoid a 10-day quarantine in the UK.