The seven time world champion's existing three year contract, following his ultra-successful first career that spanned a record-smashing 91 race wins, ends this season.
43-year-old Schumacher has faced criticism since returning from retirement in 2010, but at Monaco this year he was back on pole position, and at Valencia last time out he finished on the podium.
And on Sunday, when the great German started the British grand prix from third place, F1 chief executive Ecclestone said: "He's doing a good job; he's third on the grid here — you can't ask for much more.
"Why shouldn't he stay another ten years?" wondered the diminutive Briton, who thinks the presence on the grid of an F1 living legend is a good thing for his sport.
"If it was up to me, he would stay forever," Ecclestone is quoted by the German news agency SID.