La Liga president Javier Tebas hopes the top flight in Spain can restart on June 12th and that there would be matches every day until the end of the season.
Football has been on hold in Spain since March due to the coronavirus and La Liga started testing players last week in order to move closer to a return.
However, the league confirmed over the weekend that five players had tested positive for COVID-19 across the top two divisions in Spain.
Tebas told Spanish television network Movistar: "I’d like to restart on June 12 but we have to be prudent and it’s not just up to football, it’s also up to society, we all need to focus on complying with measures to protect health.
"The risk during games will be zero, or practically zero, because the players will be tested – with only a 5% possible failure rate – 24 hours before."
The five unnamed players who tested positive are asymptomatic and in isolation.
Three staff members also tested positive for the virus but Tebas said the number of cases was far lower than expected, insisting there would be no increase in the risk of players getting infected once matches started.
“We were expecting around 25 or 30 based on the numbers in the Bundesliga and how much the virus has penetrated Spain. Out of 2,500 people tested we have only eight positive cases, which is good news.
"Infection during a match is practically impossible as we have done a study which we’re releasing which will show there is a minimum risk in matches if we all respect the health measures."
The games will be played behind closed doors but Tebas said that La Liga have a few ideas to add to the atmosphere.
"Now that we are not going to have fans in the stadiums we are going to have some innovative ideas for broadcasting the games."
Spain has been one of the worst hit countries in Europe, with more than 25,000 deaths recorded.