The German champions have not lost in 51 games across all competitions and could wrap up a remarkable treble in two finals this week.
Leverkusen are huge favourites to see off second-tier Kaiserslautern in the German Cup final on Saturday.
But they face a much trickier task in Dublin against an Atalanta side who could also achieve the greatest ever season in their history.
A provincial club from Bergamo, Atalanta have traditionally lived in the shadow of the nearby giants AC and Inter Milan.
However, they are enjoying a golden age under Gapserini and will play in the Champions League next season for the fourth time in five years.
Yet, they have consistently missed out on a trophy to mark an era of punching above their weight.
Atalanta have not lifted silverware for 61 years having lost three Coppa Italia finals in the last six seasons, most recently to Juventus less than a week ago.
“Is it the highest point of my career? Yes, in terms of accomplishment and prestige, absolutely,” Gasperini told UEFA.com on reaching the club’s first ever European final.
“I don’t think winning a cup is necessarily always part of the parameters by which success is judged. Everyone has their own goals. When you manage to exceed them by far, as has happened at Atalanta, you still have to be very satisfied.
“If we also manage to add a cup, of course, we’ll be even more satisfied.”
The 61-year-old said Atalanta’s “world has changed” since he took over eight years ago.
Back then just surviving in Serie A was a success. Now continental football may be commonplace, but they have enjoyed two of their finest ever nights in knocking out European giants Liverpool and Marseille on the road to Dublin.
‘Golden letters’
Gasperini’s willingness to take risks with an attacking brand of football and nurturing young talent has earned the admiration of Alonso.
“He has a clear plan and built up a team with strong mentality and high quality,” said the Spaniard. “They are a top team. We’ll have a chance if we produce our best form.”
But it is Atalanta who must produce something remarkable in the Irish capital to halt the Leverkusen juggernaut.
In contrast to Gasperini’s modest playing career in the lower reaches of Italian football, Alonso was a World Cup and multiple Champions League winning midfielder with vast experience of European finals to call on from his playing days.
Yet in a career that spanned Liverpool, Real Madrid and Bayern Munich, even he has never experienced a season quite like this.
“It would be historic,” said the 42-year-old on the possibility of going the season unbeaten in all competitions.
“It would be something written in golden letters, not only in the history of our club but probably all European football. I hope we can.”
© Agence France-Presse
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