La Liga president Javier Tebas is hoping the competition 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 to date.
Spain has been one of the worst affected countries in Europe, but the death rate in the country has fallen to its lowest point in seven weeks after emerging from a strict lockdown.
Tebas has continually targeted mid-June as a resumption date for La Liga and he reaffirmed that goal on Sunday, while also insisting that there will plenty of football for fans to enjoy on a daily basis over the summer.
"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 over the weekend 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 completely clear of infection when La Liga 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."
Real Madrid players reported for their first training session in over two months on Monday, with clubs now cleared to get back on the pitch to take part in small group sessions.
Reigning Spanish champions Barcelona are also preparing to return, as they look to clinch a third successive title after establishing a two-point lead over Madrid with 11 fixtures remaining.