Unfortunately for the Glasgow side, injuries to key players mean manager Neil Lennon doesn't have the option to play a full-strength starting eleven.
Besides that, the players who are available still pose questions for him: How will 19-year-old Darnell Fisher cope if Mikael Lustig doesn't pass a fitness test? Will Anthony Stokes or Teemu Pukki start up front? And, perhaps most importantly, who will fill the creative gap in the wake of Kris Commons' injury?
The latter question cannot be underestimated. Commons is Celtic's most consistent and creative player with six goals and six assists from his 17 games. Even if he is susceptible to indecisiveness when playing in Europe, he is a massive miss.
Given captain Scott Brown is out due to suspension, it is likely Lennon will opt for Charlie Mulgrew in central midfield. The 27-year-old Scot has performed well when played there recently for club and country.
This does, however, suggest that Commons won't be replaced, per se.
Rather than having an attacking midfielder pushing forward to support the lone striker in Commons, Lennon may choose to deploy five players across the midfield to try and stifle Ajax's passing game by controlling as much of the central areas as they can.
As ever, this means Georgios Samaras will be key for the Hoops coming in from the left flank to run directly at the Ajax defence. The big Greek is also regularly used as an out-ball when Celtic are experiencing periods of pressure in these big games.
While Mikael Lustig is expected to be available, the only back-up for the Swede is teenage defender Darnell Fisher as Adam Matthews is out with a shoulder injury.
Despite impressing in the Scottish Premiership against Hibernian on Saturday, Lennon would probably rather not be forced into handing the youngster a Champions League debut in such a high stakes match.
Emilio Izaguirre is fit, however, and will take up the left-back berth in a back four beside central pairing Virgil van Dijk and Efe Ambrose.
Joe Ledley's return from a groin injury is welcome news for Celtic, even if the Welshman is unlikely to be fit enough to play a full match. He will almost certainly start in central midfield alongside Mulgrew and Beram Kayal.
The return to health and form of young Scottish international James Forrest signifies a more attacking approach down the right wing than recent European matches. Lennon has recently opted to play Matthews at right midfield, albeit the Welshman performed to great effect and plaudits.
Finally, the striker berth.
It's almost a given that only one of Anthony Stokes or Teemu Pukki will start against Ajax; Lennon could deploy Samaras as a lone striker, but the Greek has always played more effectively out wide.
Stokes has started the previous two group games, against Milan and Barcelona, and played a reasonably well lone-striker's role in each, including a brilliant piece of skill against Milan in the San Siro which almost led to a goal for the Irishman.
Pukki has scored twice in his eight games for Celtic, but hasn't started in the previous two group games at the expense of Stokes. Despite playing well on Saturday against Hibs, the Finnish international will likely start this one on the bench.
Predicted line-up (4-1-4-1): Forster; Lustig, Ambrose, Van Dijk, Izaguirre; Mulgrew; Forrest, Kayal, Ledley, Samaras; Stokes