Fink took over at Hamburg little over a year ago when they were struggling at the bottom of the table.
An immediate response to the change in coach saw the club surge up the table before Christmas and Fink, who had been keeping the expectations low, started to dream of European football back then.
What followed was the worst second half of a season in the club's history, resulting in their worst ever final league position, yet Fink is tempting fate again by starting to dream once more.
"We have a shot at Europe," he said. "If other teams slip, then we have a chance."
Only one point separates Hamburg from fifth-place Schalke, but 12th-place Werder Bremen are still only three points behind them.
Therefore, Fink is not making his desire of playing in Europe an obsession, not least after seeing last season how quickly things can change.
"We are not making Europe out to be our goal," said Fink to the Hamburger Morgenpost newspaper after his side picked up seven points in their past three games.
"Why should we? Our aim was a comfortable mid-table position and we should stick to that."