The Dutch giants, who fired coach John Heitinga at the start of the month, share with Benfica the unwanted distinction of having lost all four of their group matches this season, with the pair, who both have a distinguished history in European club competition, propping up the 36-team table.
Ajax are also struggling domestically and go into Tuesday’s match at the Johan Cruyff Arena having lost on Saturday to Excelsior Rotterdam for the first time at home in club history and slipping to sixth in the Eredivisie standings, with a gap of 14 points to league leaders PSV.
They have collected a single point from their last three home games in the Dutch league, which is their lowest tally over a three-game run at their own ground since 1975.
It was Ajax's 14th defeat in the calendar year. The only year in the club's history in which the Amsterdam side lost more was in 1964, with 17 defeats.
"A lot has to do with confidence. When things are going well, everything seems to flow naturally," interim coach Fred Grim told a press conference on Monday.
"We're looking for confidence. You can get that by winning matches. So the stakes are quite high, I think. We want to get rid of that dreadful no points behind our name."
Grim refused to accept Ajax had little chance of making the knockout stages after losing their first four games and appealed to the supporters. "Anything is still possible. We need the fans desperately. I hope we can have a good old-fashioned Champions League night."
Ajax told Grim last week he would stay in the job until at least the winter break. Before they hire a new coach, they are first looking for a new technical director and Dutch media on Monday said talks had begun with Jordi Cruyff.