Neil Lennon's side can move above AC Milan into a qualification spot in Group H if it claims all three points in Amsterdam and the Italian side loses to Barcelona at the Camp Nou.
The Dutch champions have amassed one point from their opening three group games, courtesy of a home draw with AC Milan at the start of October.
Never before has Ajax failed to win in its first three fixtures of the competition, although a victory at Amsterdam ArenA against Celtic will lift it above the Scottish club in Group H.
Frank de Boer's side does not head into the match in particularly impressive form, its only win in five outings coming against fourth-tier ASWH in the KNVB Beker.
Celtic defender Efe Ambrose anticipates a tough game in the Netherlands, but he believes all the pressure is on Ajax as the hosts look to move off the bottom of the group and avenge a 2-1 defeat when the two teams met in Glasgow two weeks ago.
"Going to Amsterdam is huge for us," Ambrose said to the Scottish Express. "It'll be a deciding game for us – every one we play from now on is crucial, a cup final, to make the last 16. We know what we're up against and we know we have to get everything right.
"It's important to believe we can do it and we're working hard to achieve our goals. We know we can't write Ajax off though. They played good football against us at home, but they didn't take their chances. We took ours."
Though it is the Scottish team that took chances, Ambrose still respects Ajax as a top opponent.
"They're a good side but the most important thing is for us to keep our heads straight and stay focused because we know if we lose it's all over. We don't want to let that happen," he said. "We're comfortable going there now, even though it won't be easy. But they know they can't lose the game if they have any chance to qualify. The better team will win the game, but I believe we're the better team."
Neil Lennon's side has lost its last two European away matches, in the playoffs at Shakhter Karagandy and against Milan on matchday one, but did emerge 3-1 victors on its last visit to Amsterdam in 2001.
A 1-1 draw at home to Dundee United on Saturday saw Celtic extend its unbeaten start to the league season to 11 matches, its longest streak since 2003-04, while Ajax lost 1-0 to Vitesse Arnhem.
Lennon will be without the services of Adam Matthews (broken collarbone) and Steve Mouyokolo (Achilles), but Georgios Samaras, Kris Commons, Mikael Lustig, Teemu Pukki and Beram Kayal could all return to the starting line-up. Nir Biton is suspended following his red card against Ajax last month.
Bojan Krkic (hamstring), Niklas Moisander (knee) and Lerin Duarte (ankle) are expected to be unavailable for Ajax.