Jurgen Klopp's men have endured a wretched start to the domestic season, winning just three of their first 12 matches to leave them in the bottom three.
Dortmund did appear to have turned the corner with a 1-0 home win over Borussia Monchengladbach on November 9, ending their visitors' unbeaten start to the campaign.
But a 2-2 draw at Paderborn followed, with Dortmund surrendering a two-goal lead and seeing Marco Reus forced off with a serious ankle injury, which is expected to keep the Germany star out until January.
Despite suffering such a bitter blow in the shape of Reus' injury, Gundogan wants an improvement from Dortmund and expects a better display than the one put on in during Wednesday's 2-0 UEFA Champions League defeat to Arsenal.
"We simply do not have enough points in the Bundesliga at the moment," he told the club's official website.
"Our goal until the winter break is now to add as many points to our tally as possible. Ideally, we would like to win all five games.
"It will still not have been a good first half of the season, but at least we would have some sort of foundation for the second half. We hope to have all our players fit again for the restart in January.
"Maybe this is the moment where we can hit the gas in the Bundesliga after slipping up in the Champions League.
"We want to do what we intended to do against Arsenal in Sunday's match versus Frankfurt."
Frankfurt are likely to be in buoyant mood, however, with Thomas Schaaf's men going into the contest on the back of a 3-1 win at high-flying Monchengladbach.
That result moved Frankfurt on to 15 points, four more than Dortmund, and they will be determined to build on that win after ending a run of four consecutive Bundesliga defeats.
Schaaf is under no illusion that it will be a tough task, regardless of Dortmund's troubles this term.
"Borussia Dortmund is and will remain a damn good team," he said.
Captain Alexander Meier agreed with his coach about the scale of the ask, but believes the victory over Monchengladbach will breed optimism.
"If Dortmund are 100 per cent and we give 100 per cent, then always Dortmund wins," he added. "[But] we have shown that we can compete against a team like Monchengladbach."
Schaaf does not have too many injury concerns to contend with and he could potentially welcome Jan Rosenthal back following a serious bout of food poisoning, though Reus missed training as a precaution on Wednesday.
Klopp, though, faces late decisions regarding the availability of Mats Hummels (ankle) and Sven Bender (hip), while Jakub Blaszczykowski (muscular injury) continues to miss out.
Nuri Sahin could be involved, however, with the Turkey international overcoming a knee injury that has kept him out all season.