Bayern need to win by a four-goal margin in order to win their group
A situation they find themselves in because of the 3-0 thrashing by a Neymar-inspired PSG in the French capital that precipitated the sacking of Carlo Ancelotti.
At the time, defending champions Bayern were also five points adrift in the Bundesliga.
But Heynckes has stamped his authority on his fourth stint at the club after Karl-Heinz Rummenigge and president Uli Hoeness turned to their 2013 treble-winning coach in their hour of need.
Bayern won nine of their ten following matches and now hold a six-point lead in the Bundesliga.
However in the Champions League, PSG arrive in Munich with a three-point lead over Bayern at the top of Group B.
Both teams are already through to the last 16, but the French have a vastly superior goal difference after five straight wins.
It means Bayern need to win by four clear goals to wrestle top spot in the clubs’ head-to-head record — a result no one in the German camp deems realistic.
“It would be an unlikely dream,” said defender Mats Hummels while chairman Rummenigge said beating PSG by such a margin is “wishful thinking”.
Heynckes sees the game as “pure psychology”.
“We want to beat them and show off what we are capable of. Everything else is far from realistic,” he added.
– Tough discipline –
“I am someone who demands a lot,’ Heynckes said on his return.
“The players will have to get used to that. Discipline is a part of life and work.”
Former AC Milan and Chelsea boss Ancelotti had lost his dressing room long before the PSG hammering.
Arjen Robben quipped that training sessions at his son’s junior team in Munich were tougher than what had become the norm at Bayern, but Heynckes tightened discipline immediately.
He insists on politeness and punctuality at all times.
Mobile phones are expected to be neither seen nor heard and training sessions start an hour earlier than under Ancelotti.
The players tidy the dressing room and eat together after training.
Heynckes is a Champions League expert, winning it twice in the three seasons he has been involved in the competition.
In 1997-98, he lifted the trophy with Real Madrid in his only season at the Santiago Bernabeu.
With Bayern, he suffered the heartbreak of a penalty shoot-out defeat against Chelsea in the 2012 final in Munich.
A year later, Heynckes lifted the trophy when Bayern became the first German club to win the treble of Champions League, Bundesliga and German Cup titles before he was replaced by Pep Guardiola.
Of his 2013 treble-winning side, Robben, Franck Ribery, Thomas Muller, Rafinha, Jerome Boateng, Manuel Neuer and Javi Martinez are still at Bayern.
Heynckes’ return has been a big plus for Mueller and Boateng who both struggled for game time under Ancelotti.
Heynckes also identified that James Rodriguez, on loan from Real, was struggling to settle in Munich, so started addressing the Colombian in Spanish.
He has also worked wonders with Arturo Vidal, having already worked with the Chilean at Bayer Leverkusen between 2009 and 2011.
The midfielder has made a vast improvement since Heynckes told him to knuckle down in training and Vidal has scored in each of his last three games.
Heynckes’ future beyond 2017/18 remains unclear.
Bayern want him to stay on, but Heynckes insists he is leaving in June, revealing he “still doesn’t have a contract” while at a fan-club visit on Sunday.