The Ukrainian side have to overturn a 2-0 first-leg deficit when they entertain Basle in Thursday's last-32 return meeting at the Dnipro Arena.
However, Dnipro have never won any European match in the new year in eight attempts in what is traditionally their mid-winter break from domestic action.
They will therefore need to break that run if Spaniard Ramos is to add a third Europa League title to his list of achievements having twice won the competition, when known as the UEFA Cup, in 2006/07 and 07/08 with Sevilla
Only current Republic of Ireland boss, Giovanni Trapattoni, has enjoyed greater success after lifting the trophy with Juventus twice and also Inter Milan.
Dnipro midfielder Ruslan Rotan said: "The first leg was a bad scoreline for us but there is still hope.
"I think we can handle it. We have to believe we can do it. We have to forget what happened in the first leg."
Dnipro will hope to reproduce the goalscoring form that brought them 16 goals in their six group matches - the best record of any side.
The good news for Dnipro is that they have won their last five European home games, a run that has included impressive victories over PSV Eindhoven, Napoli and 2010 Europa League finalists Fulham.
Another plus point for the home side is that Basle captain Marco Streller, who scored the second goal in the first leg, is set to be missing after suffering a knee injury in Sunday's 2-1 league win at Lausanne
However, his absence is likely to pave the way for a return for veteran Alexander Frei who is to retire at the end of the season.
The 33-year-old is the Swiss national side's record goalscorer with 42 goals.
A meeting with Liverpool or Zenit St Petersburg, who also lead 2-0 from the first leg against their Barclays Premier League opponents, awaits the winners in the next round.