The French tyre maker announced on its Twitter feed that it had entered a tender, launched by the governing body, before a Wednesday deadline.
Current supplier Pirelli are considered the favoured candidates, with some senior figures in the sport opposed to a switch to 18-inch wheels from the current 13-inch ones.
"Whether we'll be selected or not, we'll see," Michelin motorsport head Pascal Couasnon told motorsport.com.
"But I'd say we want to be coherent with our proposals and offer the opportunity to the teams and the drivers to have a tyre that enables everyone to express themselves and drive to the max."
Drivers regularly complain that the current rules force them to look after fast-deteriorating tyres and ease off the throttle to save fuel.
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 withdrew on safety grounds.
Formula One has had a sole supplier since then, with Bridgestone replaced by Pirelli in 2011.
Couasnon said Michelin preferred competition but the technological challenge could come from the rules themselves.
"When you are not allowed to change tyres and refuel at the same time at Le Mans, the teams need tyres that can handle several stints," he said.
"So even without rivals, you're being challenged in a technical way by your clients. That's what we want to do in F1.
"If there are several tyre suppliers, perfect. If there is only one, then a switch to 18-inch and a show made with tyres that you don't change every 10 laps is already a pretty nice technical challenge that will be useful for all of us."
Formula One's commercial supremo Bernie Ecclestone has already indicated he opposes that.
"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 criticized," he said last month.
(Reporting by Alan Baldwin, editing by Amlan Chakraborty)
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