German daily Bild reported on Saturday that the 56-year-old, who took charge in 2006, will pen a two-year extension to lead Germany's defence of the World Cup in Russia in 2018 and to the European Championships in 2020.
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Low, who led die Mannschaft to their fourth World Cup title in Brazil two years ago, is set to receive a huge pay rise to €4 million per year.
His current contract, which expires after the 2018 World Cup, reportedly earned him an annual salary of around €3 million euros.
The DFB's president Reinhard Grindel refused to comment when approached by SID, an AFP subsidiary, but he is believed to want to get the deal sealed before the German FA meets in Erfurt on November 3-4.
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If Low stays in office until 2020, his 14-year reign would make him the joint second-longest serving Germany coach, equal to Helmut Schoen (1964-78).
Sepp Herberger holds the 28-year record, from 1936-64, during which time he led West Germany to their first World Cup title in 1954.
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