The Potters are currently in eighth place with 28 points from 19 matches, but are likely to need to improve that tally in the second half of the season to qualify through the top-flight.
Only the side finishing in fifth position is guaranteed a Europa League place, although winning the FA Cup is another avenue open to Stoke.
Pulis guided the Staffordshire club into Europe for the first time in 36 years when they qualified for the 2011-12 campaign by finishing FA Cup runners-up to Manchester City.
And he is already dreaming of a return to the continent next season as Stoke head into Saturday's home clash against Southampton on the back of a nine-match unbeaten run.
"It's something we should aim for and I'm sure players and fans alike would relish the challenge if we ever got there again," said Pulis.
"That's not to overlook how tough it was with the number and timing of the games and how that affected our league form.
"It takes a lot to get used to games coming thick and fast on a Thursday and then a Sunday, not to mention the fact they kindly gave us away games in the league after virtually every away game in Europe - and they were long trips.
"But having the odds against us is what gets us going as a club, and that includes our fans."