The two European heavyweights, both runners-up in their domestic leagues, are among 10 clubs in the non-champions section of the draw.
And with the four-time winners from the Netherlands one of the seeded clubs and the 1967 winners from Scotland unseeded, there is every chance that they could end up being drawn against each other.
Ajax’s preparations have been focussed on trying to hang on to their coach and some key players.
Manager Martin Jol has been linked with the vacancy at Fulham, midfielder Christian Eriksen and goalkeeper Maarten Stekelenburg, both targets for Arsenal, defender Gregory van der Wiel who is wanted by Bayern Munich and Uruguayan striker Luis Suarez who has expressed interest in a move to the Premier League.
Celtic, meanwhile, have been preparing for the new season with a tour of the USA which coach Neil Lennon claims is the perfect preparation for the Champions League.
“If you look at the opposition, you have different types of teams,” he told Celtic’s official website. “You have Philadelphia. Then we play Manchester United, one of the best teams in the world.
“So the players will get a good look at the quality of players they will be playing in the next few weeks.
“It’s important that we avoid injury, which is why we have brought two squads with us, and also that we give the players enough playing time before we go back to the Champions League at the end of the tour.”
Even if they avoid each other, neither side is likely to be in with an easy passage to the play-off round which precedes the group stage of the competition proper.
The other seeded teams in this section - all possible opponents for Celtic - are Turkish outfit Fenerbahce, Ukraine’s Dinamo Kiev, Braga of Portugal as well as 2008 UEFA Cup winners Zenit St Petersburg from Russia.
The unseeded teams in the pot that might also face Ajax are Ghent from Belgium, Swiss side Young Boys, Romania’s Unirea Urziceni and PAOK Salonika who ousted Champions League regulars Olympiakos in Greece’s end of season play-offs.
The other section of the draw, which will see 15 ties, is for national champions.
With the second qualifying round only at the first leg stage, all 34 teams involved will go into the hat as 17 pairs where they will join Basel, Anderlecht and Copenhagen - the champions of Switzerland, Belgium and Denmark respectively.
Czech champions Sparta Prague are on course to join them after beating Latvia’s Liepajas Metalurgs 3-0 in the first leg of their second qualifying round tie.
Croatian side Dinamo Zagreb - whose only European triumph came when they won the Inter-City Fairs Cup in 1966-67 - Austria’s Salzburg, Hapoel Tel Aviv of Israel and 20-times Cypriot champions Omonia are also well placed after the first leg of their ties to make it through to the third round.
The winners of the third round ties will progress to the play-off round which will again be divided into a champions and non-champions section.
Auxerre, Sampdoria, Sevilla, Tottenham Hotspur and Werder Bremen will join the non-champions draw at the play-off stage.
The 10 winners of the play-off matches will join the other 22 in the group stage of the Champions League while the losers will go forward to the group stages of the Europa League.
The Champions League final takes place at Wembley Stadium, London on May 28, 2011.
When we choose to look away for good, we are as complicit as those at the helm of this atrocity
Over 100 people in Lebanon have been reported killed during the hostilities started on October 7