Low will step down as manager of the Die Mannschaft after this summer’s European Championships.
The 61-year-old announced his decision earlier this week, bringing down the curtain on a 15-year spell in charge of his country during which he led them to FIFA World Cup glory in Brazil in 2014.
Several names have been mentioned as possible successors to Low including Liverpool manager Jurgen Klopp and current RB Leipzig boss Julian Nagelsmann but both men have no intentions of leading the national team at this stage of their careers.
Rangnick is currently unattached and the 62-year-old says he will consider an offer from the DFB this summer if an approach is made.
"It is a job which matters to anybody," he told Sky. "In general I can imagine many things. It is a question of timing. At the moment, I am free. Should the DFB call me once I am not free anymore, it'd be too late."
He added: "I can very well imagine that a partnership with Oliver Bierhoff would be very prolific, especially for the future of German football.
Germany are in the same group with holders Portugal, world champions France and Hungary for EURO 2020, and Low would like to go out on a high after the disappointing group stage exit at the 2018 FIFA World Cup in Russia.