Evangelos Marinakis, a 52-year-old Greek businessman who also owns Greece's most successful club Olympiacos, said he was well and receiving treatment.
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"The recent virus has "visited" me and I felt obliged to let the public know," he said on social media.
"I feel good as I take all the necessary measures and I discipline to the doctors' instructions. I strongly advise all my fellow citizens to do the same. I wish all a quick recovery."
Marinakis was at Forest's City Ground for the 3-0 defeat to Millwall on Friday and reportedly met with the squad.
"Mr Marinakis was diagnosed after showing the first symptoms on his return to Greece yesterday afternoon. During his short stay in Nottingham last week he did not show any symptoms of the virus," read a statement on the Forest website.
"The club are seeking advice from medical professionals and the relevant governing bodies to ensure the correct measures are taken."
The virus has infected well over 100,000 people worldwide and killed more than 3,000. Greece has several dozen cases but no fatalities so far.
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