The Brazilians are set to open their 2018/19 campaign against Amakhosi in a massive Premier Soccer League (PSL) encounter at Loftus Versfeld Stadium in Pretoria.
However, Sundowns will be without South Africa international Jali and Liberia captain Laffor, who are both nursing hamstring injuries.
Midfield maestro Jali, who recently joined the Tshwane giants from Belgian side KV Oostende, will have to wait a little longer to make his PSL debut for the club.
Forward Laffor has resumed light training, but the former Jomo Cosmos winger is expected to miss the clash with Chiefs.
A club statement read: "Absa Premiership defending champions, Mamelodi Sundowns will be without Anthony Laffor and Andile Jali when taking on Kaizer Chiefs in the much-anticipated league opener at Loftus Stadium on Saturday afternoon."
"Both players are sidelined with hamstring injuries, with Laffor having resumed light training," the statement added.
The reigning PSL champions also disclosed that Sibusiso Vilakazi and Oupa Manyisa are both doubtful for the match.
Forward Vilakazi, who scored against Togolese club AS Togo-Port in the 2018 Caf Champions League C match at the Lucas Moripe Stadium last weekend, is nursing a minor hamstring injury.
Box-to-box midfielder Manyisa sustained a contused back during Sundowns' 2-1 victory over Togo-Port which took Pitso Mosimane's side to second place on the Group C standings.
The good news is that both players are yet to be ruled out of the match as they are set to undergo late fitness tests before the game.
"Sibusiso Vilakazi and Oupa Manyisa are doubtful for the match and will undergo late fitness tests."
"Vilakazi has a minor hamstring strain, while Manyisa suffered a contused back in the Caf Champion’s League match against AS Togo," another statement read.
The match against Sundowns and Chiefs will kick-off at 15h00.