LaLiga president Javier Tebas is hoping the league can get back underway on June 12, promising matches "every day for 35 days".
The campaign was suspended in March due to the coronavirus pandemic, which has killed more than 283,000 people worldwide.
Tebas has continually targeted mid-June as a resumption date and he reaffirmed that goal on Sunday.
"I don't know. It will depend on the phases. I wish it was June 12. It will depend on the phases," he told Movistar.
"It will depend on the spikes in the virus... the first and the second division will end at the same time.
"There will be football every day for 35 days."
It was confirmed on Sunday that five players across Spain's top two divisions had tested positive for COVID-19.
Tebas said that result was better than expected, and he hopes all players are clear when LaLiga resumes.
"We hope for the return of the competition almost no infected. If things are done as they should be, there shouldn't be," he said.
"If five infected appear at a club, it would denote some negligence. We are going to be on top [of it].
"There is a place where we have no control, which is when the players and coaches go home. They have been given a sheet of what to do."