La Liga president Javier Tebas has said there will be "zero" risk for matches to be played every day when competitive football returns in Spain.
Spain's first and second division clubs have now returned to training, with Real Madrid's players the latest to take part in individual sessions on Monday morning.
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"The risk during games will be zero, or practically zero," Tebas told Movistar. "What I ask now is the upmost focus on adhering to the health measures. If we stick to them, we'll restart the competition with very few or no infections."
Games would be played every day of the week to allow the 11 remaining matchdays in the 2019-20 season to be completed by the end of July, with teams given 72 hours rest between matches.
"I'd like the restart date to be June 12 but we have to be careful, it will depend on society as a whole," Tebas added.
Before the coronavirus pandemic, games had not been played on Monday nights, due to a legal battle between the league and the federation over the treatment of match-going fans.
It is not thought that the federation would object in this scenario, given that games will be played behind closed doors.
Tebas said that La Liga and their broadcast partners are testing various options to compensate for the lack of atmosphere, including interactive elements for viewers at home.
"As we won't be able to have fans in the stadiums, we're going to have some really interesting new ideas when it comes to football broadcasts," he said.
Ahead of a return to training, all 42 teams across Spain's top two divisions underwent coronavirus tests last week. La Liga said on Sunday that five of them had returned positive results, with all of them being asymptomatic and in the final stages of the illness.
While La Liga has not confirmed their identities, citing data protection rules, the Real Betis goalkeeper Joel Robles confirmed that he has tested positive.
Footballers who test positive will remain at home and be subjected to further testing, being able to join their teammates when they have given two negative results, 72 hours apart.
A number of others, including Real Sociedad goalkeeper Alex Remiro, announced that they had tested positive for antibodies, meaning they previously had, and recovered from, the coronavirus.
At Madrid's Valdebebas training ground on Monday, players arrived in two shifts. The first group -- including Sergio Ramos, Gareth Bale and Luka Modric -- took part in individualised training sessions at 10 a.m. local time, and the second group following an hour later.
Luka Jovic was unable to participate after Madrid announced on Friday that he had fractured a bone in his right foot.
Other La Liga clubs, including Barcelona and Atletico Madrid, had already begun training on Friday and Saturday.
A four-week process will see a gradual return to full training, with individual sessions followed by smaller group exercises as Spain's de-escalation measures continue.