The English top-flight is reportedly eyeing a resumption of the season on June 8 behind closed doors due to the coronavirus pandemic.
“Project Restart” could see the 20 Premier League clubs resume full training by May 18, allowing players a three-week “pre-season”.
Premier League chiefs, due to meet with clubs on Friday, are committed to finishing the season, with Liverpool on the brink of their first English top-flight title for 30 years.
Brighton said in a statement on Monday that the club were allowing “restricted external access to the training pitches for first-team players only, for non-compulsory individual training”.
“Players will need to book and be allotted staggered arrival slots, allocated their own area to train and expected to fully adhere to social distancing rules while doing so, and when arriving and exiting the facility,” the statement added.
A West Ham spokesman said players in apartments or without safe access to green spaces were permitted access to training pitches.
“Access will be limited to one player at a time and all sessions will be in line with government guidelines around social distancing,” he said.
An Arsenal club spokesman confirmed on Saturday that players would be allowed to return this week but access would be carefully managed.
It was unclear whether manager Mikel Arteta, who tested positive for the virus last month but has since recovered, was present on Monday.
Britain, on lockdown until May 7 at the earliest, has been one of the countries hardest hit by the pandemic, with more than 20,000 hospital deaths.