The two sides contested the 1967 European Cup final, but these days they must contend themselves with European football's secondary club competition for a chance of continental glory.
Celtic were dumped out of the UEFA Champions League at the play-off stage by Maribor, but have mounted a solid group-phase campaign and currently stand on the brink of qualification for the second round.
Ronny Deila's men face Group D leaders Red Bull Salzburg - who have already qualified - at Celtic Park, where a win will see them leapfrog their opponents and secure their own progress.
"Salzburg are a very good team so it will be a very big game at home, and hopefully we can get as many people in the stadium as we can," said Celtic defender Jason Denayer.
"It would be great for it to be full. It makes a difference to the other team as well as when you have that kind of atmosphere in the ground, it can be difficult to play well."
The other game in the group sees Dinamo Zagreb travel to Astra, who are already out.
In Group F, Inter top the table with eight points from their four matches, while the other three sides are all locked on four apiece, and Juan Jesus wants to finish the job in order to avoid any unnecessary nerves on matchday six.
"Thursday, it will be a tough match, we have to win so we are more relaxed in the pool," he said.
Victory against Dnipro at San Siro will see Roberto Mancini's men qualify as group winners, regardless of the result between Saint-Etienne and Qarabag in France.
Dinamo Moscow are one of just two sides to boast a 100 per cent record after four games, with the Russian outfit looking to extend their winning streak at home to Panathinaikos in Group E.
A win or a draw for PSV at Estoril will see Phillip Cocu's men join Moscow in the last 32.
The other side with a perfect record are Legia Warsaw, who travel to Lokeren in Group L. In the other game, a win for Trabzonspor at home to Metalist will assure the Turkish side of a safe passage.
Fiorentina are already through from Group K and Vincenzo Montella's men visit Guingamp, who will qualify if they better the result of PAOK at Dinamo Minsk.
Tottenham boast the tournament's joint top scorer in Harry Kane, who has five goals to his name, and Mauricio Pochettino will hope the 21-year-old can find the target again as they go in search of the win they need to progress at home to Partizan.
Elsewhere in Group C, Besiktas visit Asteras Tripolis, while in Group J, AaB host Steaua Bucharest and Dynamo Kiev welcome Rio Ave.
In Group H, victory for Everton at Wolfsburg will see them qualify as group winners, while Lille and Krasnodar will vie to keep themselves in contention when they meet in Russia.
The top two in Group G clash when reigning champions Sevilla visit Feyenoord, while Rijeka take on Standard Liege. In Group I, Sparta Prague take on Napoli and will secure qualification if they better Young Boys' result at Slovan Bratislava.
Borussia Monchengladbach of Group A take on Villarreal in Spain, with Zurich hosting Apollon and in Group B Torino host Club Brugge and Copenhagen visit HJK.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1