Frank de Boer's men earned their place in the qualifying rounds of the Champions League as a result of their second-place finish in Eredivisie last term.
Ajax were drawn against Vienna in the third qualifying round, and claimed a 2-2 draw in the first leg of their clash, but were defeated 3-2 by the Austrian club at the Amsterdam ArenA to crash out of the competition.
It was the first time the Dutch side had not reached the Champions League proper since the 2009-10 season, and they were forced to battle past Jablonec to reach the group stage of the Europa League.
The club have won the competition twice in their history, the last of which came in 1992 under the management of Louis van Gaal.
Despite their exit from the Champions League, Ajax have enjoyed a strong start to their season in Eredivisie as they have dropped just two points in their opening five matches, which came in their last outing against FC Twente.
De Boer will be hopeful that his side can continue their positive start to the campaign in front of goal against the Bhoys after scoring 14 times in their first five league matches, while the two goals they conceded against Twente were their first since the start of August.
Recent form: WWWWD
Recent form (all competitions): WWWDWD
Celtic also exited the Champions League in disappointing circumstances as they lost to Malmo in a 4-3 aggregate defeat, resulting in the club missing out on the group stage for the second straight year.
The loss was a huge blow for Deila and his men as they looked to be in a good position to reach the group stage when they took a 3-1 lead in the first leg of their clash at Celtic Park, but a late Jo Inge Berget strike switched the momentum in the tie.
Celtic did respond to their exit with a solid 3-1 win over St Johnstone, but they fell to their first league defeat of the campaign against 10-man Aberdeen last week at Pittodrie. The defeat has left them five points behind the Dons after seven matches this season.
Second place in the Scottish Premiership is an unusual position for the Bhoys to be, and as a result slight pressure has begun to grow on Deila, especially in the manner of his side's exit from the Champions League.
The Norwegian will be hopeful that his side can get back to winning ways against Ajax to rebuild some confidence and establish themselves in the competition.
Recent form: WDWWWL
Recent form (all competitions): WWWLWL
Tyler Blackett is expected to continue at centre-back alongside Boyata after making his debut at Pittodrie, following the departure of Virgil van Dijk, as Charlie Mulgrew and Mikael Lustig will operate in the full-back positions.
De Boer may make changes to his side by starting the players that inspired Ajax's second-half comeback against Twente. Viktor Fischer, Yaya Sanogo and Ricardo van Rhijn could all feature at the Amsterdam ArenA after their impressive substitute appearances.
Ajax possible starting lineup:
Cillessen; Tete, Viergever, Veltman, Van Rhijn; Bazoer, Klaassen, Gudelj, Sinkgraven El Ghazi, Fischer
Celtic possible starting lineup:
Gordon; Lustig, Boyata, Blackett Mulgrew; Biton, Brown; Mackay-Steven, Johansen, Forrest; Griffiths
Head To Head
Over the course of history, the Bhoys hold the edge in this fixture by winning four of the eight clashes, while Ajax have only managed three wins.
We say: Ajax 2-0 Celtic
The Dutch side have been strong at home this season and are currently on a good run of form, appearing to be very confident in front of goal. Celtic have been nervy at the back and lacked a cutting edge up front in their defeat to Aberdeen. So, Ajax should have enough to claim the win.