Rodgers said that both he and his wife tested positive after displaying symptoms, but have recovered.
He told BBC Leicester Sport: "Me and my wife had it just after [the season] broke up. A week later I really started to struggle, I had no smell and no taste.
"I had no strength, and I really struggled, and my wife was the same as well. I got tested and we both had it. I could hardly walk.
"It reminded me of climbing Mount Kilimanjaro, as you climb higher you get more breathless. Walking 10 yards felt very different. I went for a run, and I just couldn't do it.
"I felt really weak, had no real appetite, and had a weird sensation for three weeks of having no taste."