Heynckes returned to Bayern for his third spell in charge of the club in September, replacing Carlo Ancelotti after previously retiring in 2013.
Heynckes was installed until the end of the season, but reports continue to suggest the club's hierarchy will try to convince him to stay for a further year, after making such an impact.
And Matthaus believes the dream scenario would see Heynckes stay until the end of the 2018-19 season before being succeeded by Low, who will preside over Germany's World Cup defence in Russia later this year.
Speaking to reporters, Matthaus said: "It would be my dream for Jupp continues for one year and then Joachim Low takes over the Bayern manager role in 2019 after a successful World Cup and a sabbatical year.
"If Heynckes can bring family and work together for another year then I see a chance [that he stays]. If it doesn't work with the family, he will finish his job after this season."