The governing International Automobile Federation (FIA) said on Wednesday that the two had met the requirements to become approved bidders and had been submitted to the sport's commercial rights holder.
Ecclestone, the commercial supremo who represents controlling shareholders CVC, will conduct negotiations with both and make a decision for the FIA's World Motor Sport Council to approve.
The FIA body's next scheduled meeting is on Sept. 30 in Paris.
Michelin withdrew from Formula One in 2006, a year after a farcical U.S. Grand Prix that went ahead with only six cars after all the Michelin-equipped teams pulled out on safety grounds.
The sport has had a sole supplier since then, with Bridgestone replaced by Pirelli in 2011.
Ecclestone indicated earlier in the year that he favoured retaining Pirelli, who also invest heavily in trackside advertising.
"All Michelin would do is make a rock-hard tyre that you could put on in January and take off in December because they don't want to be in a position where they can be criticised," the 84-year-old Briton said in May.
Whereas the Pirelli F1 compounds have been engineered to degrade, in a move aimed at increasing strategy options and encouraging overtaking, Michelin have said they are not prepared to make a tyre that did not last.
Michelin motorsport head Pascal Couasnon told Reuters last month that the French company also had no interest in supplying tyres to Formula One unless the sport agreed to change the specification from 13 inch to at least 18 inch.
The current FIA tender document opens the way for an increase in diameter "if the tyre manufacturer feels there may be advantages to the competitors by doing so."
Formula One is in Hungary this weekend for the 10th race of the season.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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