Liga President Javier Tebas hopes that the Spanish elite will resume on June 12 and says that coronavirus tests will mean "virtually zero" risk to players during the matches.
The league said on Sunday that five players tested positive for the virus in the two main Spanish divisions.
La Liga started testing players last week as it plans to resume training and play behind closed doors.
"I would like to [the restart date] as of June 12, "Tebas told Movistar.
"But we have to be careful. This will depend on many factors such as a potential increase in infections, factors that do not depend on football but on Spanish society.
"The risk during the matches will be zero, or practically zero, because the players will be tested – with only 5% of possible failures – 24 hours before."
Tebas added that the Spanish second division would resume at the same time and that the national competitions should be finished by July 31, the European competitions ending in August.
The Spanish said that "interesting and revolutionary" broadcast alternatives would be used since there will be no fans at the matches and there will be "football every days "once the league has restarted.
A number of clubs, including Barcelona, started individual training last week.
The five anonymous players who tested positive are asymptomatic and isolated.
They will continue to be tested and will only be able to resume training if they return two consecutive negative results.
Tebas said "between 25 and 30 positive cases" are expected, adding that five positive tests are "good news for the football industry".
Real Madrid captain Sergio Ramos added: "Players and football can help the economy to function again, to get out of complicated situations.
"Football is secondary at the moment, but it can be a distraction for people who are suffering."
Spain was one of the most affected countries in Europe, with 26,621 deaths and 264,663 infections as of May 11.