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"I could hardly walk and it reminded me of walking up Mount Kilimanjaro," the 47-year-old told BBC Radio Leicester.
"We had a week off when we were supposed to play Watford [14 March] and then the week after that, I started to struggle.
"For three weeks I had no smell or taste.
I had no strength, and a week after, my wife was the same. We were tested and both of us were detected with the virus.
Rodgers climbed Kiliminjaro for charity in 2011 and says his breathing difficulties was comparable to scaling the 5,895m mountain.
"It reminded me of when I climbed Kilimanjaro. The higher you went the more you suffered with acclimatisation and the harder it was to breathe," he added.
"I remember trying to run for the first time [after becoming ill] and it was hard to go 10 yards. I had no real appetite and it was a weird sensation of eating food without ever tasting and smelling what it was.
"It has made me really appreciate being fit and healthy."
Inter hold out for €111m as Barca close in on Lautaro signing – Euro Papers
Arsenal's Mikel Arteta was the first Premier League manager to test positive for COVID-19 in March.
Leicester are now back in contact training with their first Premier League game back expected to be played on the weekend of June 19-21.