Left-back Cole has a hamstring injury, while central defender Cahill is sidelined with a knee injury.
The Russian visitors will be without striker Alexander Ryazantsev and French midfielder Yann M'Vila, who both miss the trip to London through injury. They also have fitness concerns over midfielder Alan Kasaev, who was ruled out of their weekend league win against Lokomotiv Moscow.
Chelsea boss Rafael Benitez is expected to reshuffle his starting XI as the Blues prepare for their third match in just six days.
He made seven changes for Monday's FA Cup quarter-final win against Manchester United, but the move paid dividends as Chelsea reached the competition's semi-finals for the fifth time in seven years.
Benitez will be forced to make at least two changes from that team due to the absences of Cole and Ba. Cole, 32, could be sidelined for up two weeks after being substituted after 21 minutes against United and Cahill looks set to miss next week's return leg in Russia.
"I have to pick a team that can win any game," said Benitez. "You have to approach the next game like the most important game.
"Sometimes we will pick one team for one game and we will change three, four, seven players for the next one. That is the way to compete and to be capable of winning in every competition.
"Rubin can score goals away, they will try to do that. It will be tough. It's important to score and to do well."
Rubin are competing in the last eight of a European competition for the first time after beating holders Atletico Madrid in the last 32 and their Spanish compatriots Levante in the last round.
Rubin manager Kurban Berdyev believes Chelsea are the toughest quarter-final opponents they could have faced.
"However, for us, it will become just an extra motivating factor that will make this tie more attractive," said Berdyev.
"We will try to give our best in these matches against a top English team to perform at their level."
Predicted Line Up: Chelsea
Chelsea ? Petr Cech, Cesar Azpilicueta, John Terry, David Luiz, Ryan Bertrand, John Obi Mikel, Frank Lampard, Eden Hazard, Oscar, Juan Mata, Fernando Torres.
Source: DSG
Source: DSG