Frankfurt lie two points ahead of Hamburg and, taking into account their significantly superior goal difference compared to their rivals, realistically need just a draw from their final game against Wolfsburg to clinch sixth spot.
Hamburg, meanwhile, need to beat Bayer Leverkusen to stand any chance of snatching a place in the Europa League.
Despite the odds being against his side, Fink is in bullish mood heading into the final round.
"We have a lot to gain, but nothing to lose," he is quoted as saying in the Bild newspaper.
"Frankfurt need to get at least a draw against Wolfsburg and that is psychologically difficult.
"For us, the situation is easier. Furthermore, Wolfsburg are no easy opponents at the moment."
Defender Marcell Jansen added: "We've got to do our own job first and win this tough game."