The restaurant is experimenting with delivery services in some countries "in a big way," as well as in densely populated areas in the U.S., Thompson said. About 20 percent of McDonald's outlets offer delivery service, and nearly 50 percent are open 24 hours, the financial blog Seeking Alpha said.
"Delivery is a big, big opportunity, particularly in areas where you don't have drive-throughs," he added in his interview with CNBC.
While some markets around the world already offer all-day breakfast, Thompson said the company is considering introducing it to other United States' markets.
"We have the focus on our existing menu, but we have looked at breakfast across the day," Thompson said.
Although Thompson did not release specific information about a potential loyalty program, he said he loves the idea and that customers could see it in the future.
The changes could come as McDonald's evolves to meet the changing demands and tastes driven by millennials, Thompson said. Around the country, taste preferences are shifting toward healthier options and more complex flavors, he added.