The Reds would've been crowned Premier League champions by now for the first time in their history if not for the global health crisis.
Premier League chief executive Richard Masters this week described the June 12 date as a "staging post" and said there would be flexibility in fixture scheduling.
The Hornets already had three people - Adrian Mariappa and two staff - receive a positive result in the English Premier League's first round of testing and forced into isolation. "It's great for everybody, including the fans, to see our players back on the training ground", Masters told BBC Sport on Friday.
Masters said he recognised the need for "contingency plans" and admitted "curtailment is still a possibility".
It is another blow for the club who also have several players, including captain Troy Deeney, staying away from training due to ongoing safety concerns.
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Matches will be played behind closed doors due to the virus, but Masters said the Premier League want games to be staged at clubs' normal stadiums rather than neutral venues, which was the original suggestion. "I would be comfortable to return to training".
Premier League officials, medical experts and representatives from all 20 sides held talks on Monday via a video conference call and agreed to stage one - non-contact and in small groups - of the return to training protocols.
The UK government has yet to give the go-ahead for contact training, which would be a major step towards getting the league back up and running.
"We are in a part of the world where we hope at some point people will be able to sit next to each other and enjoy the experience of a sporting event but that seems like a long way off at the moment", the American said in an interview shown on Sky Sports on Friday (May 22).
"We have to respect those players that take a decision not to return to training, that is their prerogative".
"Everybody's situation is different but ultimately, for me, I feel very safe here at the training ground, otherwise I wouldn't be here".