The Dutchman lifted the club from the second division into the top flight for the first time in its history last term, and after taking nine games to register their first win, leading them to safety is nothing short of a miracle.
Yet differences of opinion with the club's chairman Walther Seinsch, who has yet to offer Luhukay's assistant coaches new contracts for next season, appear to have convinced him to call it a day.
Several German newspapers claim Luhukay has already tendered his resignation, but he would not confirm those reports at a press conference today.
"Nothing has been decided yet," he said. "We will make an announcement when the time is right once talks have been held."
That time could be immediately after Augsburg end their first campaign in the Bundesliga at home to Hamburg tomorrow, when the team is expected in the city centre to celebrate avoiding relegation in front of the town hall.
Hamburg also have reason to celebrate tomorrow [Saturday], even if avoiding relegation was not the aim they had at the start of the season.
Going into the 50th season of the Bundesliga as the only club to have never been relegated is nevertheless something to be proud about.
"I am just glad that I am not the first director of sport to be relegated with Hamburg," said Frank Arnesen.
"I am convinced that we will make a step or two in the right direction next season, given the experiences from this campaign.
"We want to rise and European football has got to be our aim. We want to finish in the top eight."
Mladen Petric will not be part of the squad next season and, after being given a send-off in Hamburg last weekend, he is unlikely to figure tomorrow [Saturday] as coach Thorsten Fink already turns his attention to next term by only considering players he should have at his disposal.