The Verdict: Need More Info
A discretionary permit for self-funded retirees exists, but there is no published income threshold. Get private health insurance quotes, then ask the Ausländerbehörde where you plan to live what it expects.
Germany has no retirement visa. The legal basis is a general clause, Section 7(1) of the Residence Act, which allows a permit "in justified cases" for a purpose the Act does not name. Retirees are granted permits under it, but nothing obliges the authority to say yes, so no answer here can be better than possible.
No income threshold is published, and we will not invent one. The local Ausländerbehörde weighs your pension, savings and investments against the cost of living where you plan to settle and the risk that you will later need public support. A lifelong pension counts for more than savings of the same annual value, and practice varies between cities.
Comprehensive private health insurance meeting German requirements is where marginal cases most often fail. Premiums rise steeply with age, so price it before anything else.
Ties to Germany strengthen a "justified case": family there, earlier residence, property or some German. If a parent or grandparent held German citizenship, check the Citizenship by Descent quiz first, as that route needs no money.
The permit is renewed on the same discretionary basis each time. Citizenship needs five years' residence, German at B1 and the naturalisation test.