Earlier, Bernie Ecclestone had said that although the F1 Commission approved the controversial shakeup, the software-writers at Formula One Management would run out of time to be ready for the first race of 2016.
However, Germany's Auto Motor und Sport reports on Wednesday that a compromise solution has been found, following a meeting between F1 race director Charlie Whiting and team bosses in Barcelona.
"Q1 and Q2 will be the new elimination process," said respected correspondent Michael Schmidt. "(And) Q3 will take place according to the old system."
It means that in Q1 and Q2, after seven minutes of running, drivers will be eliminated one by one every 90 seconds. The top 8 will then be left to fight it out for pole in Q3, as per the existing 'knockout' format.
The compromise was found because Ecclestone reportedly feared that introducing his preferred system mid-season was not ideal for a professional sport.
The change must be rubber-stamped by the World Motor Sport Council on Friday.