The Hoops lost their opening two Group H matches, away to AC Milan and at home to Barcelona, leaving Neil Lennon's men bottom of their section.
It is widely thought that the double-header against the Dutch side represents Celtic's best chance of getting points on the board to rescue hopes of reaching the last 16 for the second successive season or, failing that, a place in the Europa League.
However, speaking at Celtic Park where he was helping to launch a book about the former Celtic player from the 1930s, Malcolm McDonald, the ex-Hoops midfielder said: "People are thinking Ajax will be third best of the three but sometimes when you know the opposition it is different, Celtic knew Barcelona and they handled them really well.
"Ajax will be fresh, they will be looking forward to playing here in a fantastic atmosphere, so they will possibly play as well as the other two teams.
"They have always been one of the top European clubs but I think people are looking at them and thinking that they are maybe the weakest one in the group.
"But I think they might surprise a lot of people when they turn up here at Celtic Park, they will still be a good football team. It will be a tough game."