La Liga has been suspended since March but started testing players last week as it plans to resume training and play matches behind closed doors.
Five players from across Spain’s top two divisions tested positive on Sunday but Tebas says regular testing will mean “practically zero” risk to players during games.
“I’d like it [the restart date] to be 12 June,” Tebas told Movistar.
“But we have to be careful. It will depend on many factors such as a potential rise in infections, factors which don’t depend on football but on Spanish society.”
Spain is one of Europe’s worst-hit countries but has begun easing its strict lockdown. Some Spaniards can meet at bars and restaurants from today.
-BBC