Having initially retired upon guiding Bayern to an historic treble in 2012/13, Heynckes answered the call to take over as interim coach shortly after Carlo Ancelotti was sacked in September.
With Ancelotti overseeing a mixed start to the season, Heynckes has turned the fortunes around. The team has taken 36 points from a possible 39 since he took over and now sit as many as 16 points clear at the top of the table as an unprecedented sixth straight domestic title awaits.
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Bayern are also progressing in the DFB Pokal, while ultimately only head to head goal difference with Paris Saint-Germain kept them topping Champions League Group B. A Last 16 tie against Besiktas now awaits in February and March.
"We are trying to tell [Heynckes] that his mission at Bayern is not over," Hoeness is quoted as saying by SportBild.
Bayern want Heynckes to oversee a 'transition' at the club as veteran players like Franck Ribery and Arjen Robben reach the end of their illustrious careers. And Hoeness feels it needs to be done by someone older who has already has the respect of all the players.
"Jupp is the one to create the transition from the older to the young players. Imagine, a young coach at the age of 35 telling Ribery: 'I'm not starting you today'. We trust this transition to Jupp who has done a job with the highest distinction," the president explained.
"I hope to convince him to stay one more year. There is no plan B!"