Having being held to a 1-1 draw in Amsterdam a fortnight ago, the Dutch side are unlikely to reach the semi-finals and are only too aware that their chances of returning to the competition next season are slim indeed. They lie fourth in the Dutch League - 16 points behind the leaders, PSV Eindhoven.
For Ajax, this season's problems have been a combination of the old and new. The familiar one has been the continuing loss of key players. Last summer saw the departure of Edgar Davids, Finidi George, Michael Reiziger and Nwankwo Kanu. These players have not been properly replaced, and the side has been left unbalanced.
On the left of midfield, the elegant Richard Witschge is no substitute for the driving power of Davids. On the right wing, the new man, Tijani Babangida, has more pace than his fellow Nigerian, George, but lacks his vision and technique, so that attacks have a tendency to peter out.
Then there have been the injuries. Most of the team are internationals, so players who were already exhausted by last season's campaign played in Euro 96 and began this season with barely a fortnight's rest.
As a result, the team has been upset by persistent injuries to key men. Patrick Kluivert, Jari Litmanen, Danny Blind, Frank de Boer and Witschge have all missed large parts of the season and Louis van Gaal, Ajax's respected coach, has been forced to use 28 players in the league campaign, and has rarely been able to field a full-strength team.
The injury problems have been exacerbated by the controversy surrounding the Arena, their futuristic new 50,000-seat stadium where, because of technical problems, the pitch has had to be relaid five times in eight months. Ajax's normally fluent passing game requires a perfect surface, but the Arena pitch has often resembled a desert.
Ajax's problems seem certain to get worse rather than better in the short term. The Bosman ruling means that not only do Ajax not get paid for some of the players they have nurtured since childhood, they now find Italian scouts haunting their youth team (Udinese recently signed a 19-year-old who had played only one game for the first team).
The loss of talent will continue this summer, starting with the brilliant but abrasive Van Gaal. No one knows where he will be next season, though, the feeling in the Netherlands being that it is now unlikely to be Barcelona, where the treatment of Bobby Robson is said to have appalled him.
Milan have already signed the brilliant Kluivert, who is still only 20, and the defender Winston Bogarde for next season - leaving Ajax without a penny, as happened with Davids, because the players' contracts have expired. Transfer speculation swirls around the De Boer twins, Frank and Ronald, and the winger Marc Overmars, who is still not back to his best after a long injury. If Overmars and the brothers do go, it would leave Ajax with just three members of the team which won the European Cup in 1995: the sweeper and captain Danny Blind, the Finnish midfielder Jari Litmanen, and the goalkeeper Edwin van der Sar.
The task of returning the team to championship winners will fall to Morten Olsen, a great player for Denmark in the 1980s but not yet a successful coach. Despite all their problems, Michael van Praag, the Ajax president, remains optimistic. "Every year one or two big names leave. It is sad, especially for me. But we are used to it. There is absolutely no panic," he said.
Ajax's annual budget is just over pounds 20m, which the club is trying to increase to pounds 100m. It is a lot for the Netherlands, but small by comparison with Europe's giants. "In southern Europe, clubs can lose millions of dollars every year and still buy players because they get money from I don't know where," Van Praag said. "We don't think we will ever come to the same level as them budget-wise, but we try to narrow the gap. But we have something they do not have. Our school."
Van Praag is "anxiously awaiting" Uefa proposals for a new system to limit the Bosman damage by allowing clubs to sign contracts with youth- team players with an option for a further three years. "All clubs could agree on that and it would be better than nothing."
Meanwhile the club is determined to hang on to its established stars. "We signed contracts last year with Overmars until the year 2000 and with the De Boers, at their own request, until 2004. We are not going to allow them to break their contracts so they are not leaving," Van Praag insisted. "People always say the team will break up, but we always seem to survive because of our scouting system and the good way we educate our players. If we are not in the Champions' League next season it would be a pity, but it would not be the end of the world."
DEATH OF THE DREAM TEAM: THE PLAYERS WHO WON THE 1995 EUROPEAN CUP FINAL
Edwin van der Sar
Now 26, Ajax. Loyal goalkeeper with long contract. Will be staying.
23, Milan. Defender took Bosman-style free transfer in 1996.
35, Ajax. Veteran sweeper has been troubled by injury and will decide about retirement in the summer.
Frank de Boer
26, Ajax. Defender. Has long contract but rumours persist. Has been linked with Parma, Sampdoria, Barcelona and Arsenal.
34. Legendary midfielder retired in 1995. Now occasional TV pundit happily running his underwear company.
20. Real Madrid. The "little general" who made his European debut aged 16, was sold to Sampdoria in 1995 for about pounds 1.5m and is now flourishing at the Bernabeu.
24. Milan. Thrusting midfielder took Bosman-style free transfer in 1996. Now has badly broken leg.
26, Ajax. Vital attacking midfielder has been linked with several clubs in Italy but has long contract and is expected to stay unless the team disintegrates completely.
25, Real Betis. Brilliant winger sold in 1996 for about pounds 4.5m.
Ronald de Boer
26, Ajax. Midfielder. Like his twin brother, has long contract - but will it hold him?
23, Ajax. Winger. Refuses to answer questions about where he will be next season. Known to want to play in England and persistently linked with Arsenal and Manchester United.
20. Internazionale. Striker sold for about pounds 1m in 1996, but career may be over despite recovering well from surgery to repair a heart defect.
20. Ajax - but only for another couple of months. The biggest blow of all. World-class striker who could become a second Marco van Basten has, like defender Winston Bogarde, signed to play for Milan next season. Because of the Bosman rulings, Ajax will not get a penny.
Louis van Gaal (coach)
45. Leaving Ajax at the end of the season to "spread his wings" - but only he knows where he will be flying. Despite Van Gaal's anger over the treatment of Bobby Robson, most people still think it will be Barcelona.
1995 European Cup final
Ajax 1 (Kluivert 85) Milan 0 (at Ernst Happel stadium, Vienna).
Ajax: Van der Sar; Reiziger, Blind, F De Boer, Seedorf (Kanu), Rijkaard, Litmanen (Kluivert), Davids, George, R De Boer, Overmars.
Milan: Rossi; Panucci, Costacurta, Baresi, Maldini, Donadoni, Albertini, Desailly, Boban, Massaro (Eranio), Simone.