Spain's Health Ministry will allow La Liga players to be tested for coronavirus from Monday (May 4) as they close in on a return to play.
The country's Higher Sports Council (CSD) has green-lit a return to training for professional sports people starting from next week.
However, the CSD stipulated that the measures are dependent on the evolution of the pandemic.
La Liga president Javier Tebas has always had in mind a potential return to action in June.
Both AS and Marca claim that La Liga is planning to start carrying out the tests between Tuesday and Thursday of next week, allowing players to begin individual training programmes.
Valencia have confirmed they will be testing their players on those dates.
Cadena Ser report that group training would hopefully start on May 18.
However, CSD president Irene Lozano has warned, "We do not know when LaLiga can restart.
"At the moment we are going to the stage with training and for the matches we are going to go 'match by match'.
"For them to be played you have to see the evolution of the training stage.
"At the moment it is totally impossible to set a date for the return of the competition, which will depend on the evolution of the pandemic."
Barcelona midfielder Ivan Rakitic is among those keen on a return to the pitch.
The Croatian told Marca, "I want to play.
"It is evident that we must try to return with the best sanitary guarantees but we must also know that they will never be 100 per cent."
On Thursday, French league officials announced the end of the 2019-20 Ligue 1 season, in the process handing the title to Paris Saint Germain.
The Spanish Football Federation (RFEF) said earlier this month they would also parse out European places based on the current La Liga standings.