Nagelsmann, whose sacking in March 2023 led to Tuchel's arrival, was tipped to return to Bayern, but has now extended his contract with Germany until 2026
"Our players Casemiro and Hazard have given positive results in the COVID-19 tests carried out on Friday morning," Real said in a statement.
The club said that all other first-team players and coaching staff, as well as the club employees who work directly with them, had returned negative tests.
Real defender Eder Militao had tested positive for COVID-19 earlier this week and was forced to miss Tuesday's 3-2 victory against Inter Milan in the Champions League.
Real, who are a point and place behind La Liga leaders Real Sociedad with a game in hand, face 13th-placed Valencia on Sunday.