The Citizens were knocked out in the last 16 of the EFL Cup on Wednesday, losing 2-1 at Tottenham Hotspur, and Savinho was forced off on a stretcher with an ankle injury midway through the second half of that match.
Manuel Akanji picked up a groin problem during the warm-up and was forced to pull out of the starting lineup. The Swiss defender and Savinho have emerged as major doubts for Saturday and will be assessed ahead of kickoff, as will Josko Gvardiol who picked up a knock at the end of Wednesday's game.
All three players could enter a packed treatment room including Rodri (ACL), Oscar Bobb (leg fracture), Kevin De Bruyne (groin), Kyle Walker (knee), Jeremy Doku and Jack Grealish (both unspecified) who will all miss the trip to Bournemouth.
Pep Guardiola's squad is now down to its bare bones, but the Catalan coach could recall up to five players who were not named in the starting lineup in midweek, including goalkeeper Ederson who is set to replace Stefan Ortega between the sticks.
If Gvardiol is passed fit to play on Saturday, he is expected to return on the left side of defence and could line up next to John Stones and either Ruben Dias or Nathan Ake, while Rico Lewis continues at right-back.
Another set to start is midfielder Mateo Kovacic, who could either replace or partner Ilkay Gundogan in the middle of the pitch, while Bernardo Silva could operate on the right flank if Savinho is not deemed fit to feature.
James McAtee and Nico O'Reilly both impressed in midweek, but they will likely drop out of the first XI on Saturday, while Phil Foden and Matheus Nunes - the latter of whom scored against Spurs - could retain their starting spots as a rested Erling Haaland returns to lead the line.
Manchester City possible starting lineup: Ederson; Stones, Dias, Gvardiol; Lewis, Kovacic; Bernardo, Gundogan, Foden, Nunes; Haaland