Stevens was on Tuesday unveiled as the Royal Blues' new coach in place of Ralf Rangnick, who resigned a week ago due to health reasons.
And although he does not want to dwell on the past too much, he does of course remember leading Schalke to glory in the UEFA Cup 15 years ago, and he knows what winning this competition did for his own career.
"When I started out with Schalke back then, I was a nobody," he said.
"With the success I had here, my name became more widely known in the Bundesliga.
"But what happened in the past no longer matters. Now we are aiming for new successes.
"I spent six years of my career with Schalke and I know why they say 'once Schalke, always Schalke'.
"You take a bit out of every club in your career, but you take a lot more from here. I am really motivated to get started again."
Stevens' first training session in charge on Tuesday morning did not go exactly to plan, however.
Striker Raul left the field prematurely with a sore ankle and defender Atsudo Uchida did not last the whole session either due to a muscle strain.
Regular goalkeeper Ralf Fahrmann was not present at all due to a stomach upset.
"Raul took a knock last week and he just went over on it today [Wednesday]," reported Stevens. "He has a bit of pain and we did not want to take any risks."
Schalke cannot afford to be too cautious, though, as they only drew their first pool game against Steaua Bucharest a fortnight ago.
Opponents Haifa, on the other hand, defeated Larnaca 1-0 to top the group and they confirmed their convincing form with a 5-0 win over Hapoel Ironi Nir in the Israeli Premier League at the weekend.
That win lifted them up to fourth in the standings ahead of their next league clash with leaders Maccabi Tel Aviv.
That game has been put back to Monday night to enable Haifa more time to recover from Thursday night's match at the Arena AufSchalke, and also allow them to focus on making it another successful European night.