The Paris Saint-Germain forward and team-mate David Luiz are reportedly fearful of returning to the city after Friday's terror attacks, although the Brazilian returned on Monday following international duty.
Coordinated attacks on the city led to at least 129 people being killed.
Speaking ahead of Uruguay's World Cup qualifier against Chile on Tuesday, Tabarez was unwilling to be drawn on the reports surrounding Cavani, who remains with the national squad.
"I haven't spoken with him. I didn't know what you just told me," he said.
"He is a player who lives in that city, so it's normal that he's been affected by it."
Tabarez added: "It's a thing that doesn't have anything to do with the match. So I won't speak about it. And if I knew anything I wouldn't tell you."
Uruguay sit third in qualifying after taking six points from their opening three games, but they were beaten 2-1 by Ecuador in their last outing.