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"The results of a test done today showed a positive result for coronavirus," Terim said on Twitter.
"I'm in safe hands at the hospital. Don't worry. Hopefully I'll communicate more as soon as possible," Terim added.
Dubbed "Emperor", 66-year-old Terim, the former Turkish national boss, coached Galatasaray in three different stints (1996-2000, 2002-2004 and 2011-2013).
He picked up the role for a fourth time in December 2017.
Turkey has officially recorded 1,236 cases of the new coronavirus while 30 people have died, according to the health minister late Sunday.