The Belgian and Turkish clubs sit five and six points adrift of second-placed Arsenal with two games to play, but will be hoping the stuttering Londoners slip up against Group D's dominant leaders Borussia Dortmund this week.
Should Jurgen Klopp's side leave the Emirates Stadium with three points, a win for either Gala or Anderlecht at the Stade Constant Vanden Stock would keep them in contention going into the final matchday.
However, a repeat of the sides' 1-1 draw in September would eliminate the pair.
Besnik Hasi's side head into the game having dropped points in the Jupiler League for the fourth time this season directly ahead of a Champions league game.
Saturday's 3-1 defeat at Charleroi saw Anderlecht relinquish top spot domestically and though Hasi - who claimed in jest he would happily change all 11 players - admits looking too far ahead may be an issue, he has backed his team to respond in the best way.
"Maybe it's been a factor [looking ahead to Champions League fixtures]," he said.
"But if that is the case, this is not the right mindset to have because if we had won we would have approached the visit of Galatasaray with a positive outlook.
"Maybe it will be a good thing, it will bring everyone back down to earth.
"I have no doubts about the group. They are young and they have many qualities.
"I'm sure they will show this on Wednesday."
Hasi will have to make do without Matias Suarez (knee), but will give Steven Defour every chance to recover from a calf injury.
While Anderlecht will rely on Gala beating Arsenal on matchday six if they are victorious, Cesare Prandelli's side face a huge task to overtake the Londoners - needing to overturn a 4-1 defeat to win their head-to-head battle as well as the right results this week.
Prandelli is under huge pressure after an embarrassing 3-0 defeat to Trabzonspor on Saturday also saw Gala give up top spot in their domestic league.
The Turkish side have conceded four goals in each of their last three European outings and defeat on Wednesday would see them unable to overtake Anderlecht to make the UEFA Europa League as the pool's third-placed side.
Gala fans were heard calling for Prandelli to resign at the weekend and defeat in Belgium will do his chances of remaining in the hotseat no favours.
The Italian will be without influential midfielder Blerim Dzemaili as he serves a one-match suspension.
