Jurgen Klopp's side won the Champions League in June of a year ago and some 750,000 fans lined the streets of Liverpool for an open-top bus parade through the city in celebration.
"Curtailment is still a possibility and so what would happen in that environment is something we are yet to discuss with our clubs", Masters told BBC Sport.
And Werner has revealed plans to have the same sort of arrangement if and when they're confirmed as Premier League winners.
"The most obvious choice for me is the end of June".
Players returned to training in small groups this week.
The Premier League's chief executive, Richard Masters, has said he is "as confident as we can be" about restarting in June.
Most top-flight stars are back at work though, amid stringent testing and social distancing measures, and Masters said he would also have agreed to train, had he been a player.
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"Most importantly, if the scientists and the government feel it's unsafe there will be no football, but hopefully we can figure out a way to give people some enjoyment".
Meanwhile, Chelsea midfielder N'Golo Kante is prepared to sit out the remainder of the season, if it resumes, after expressing concerns over returning to training, British media have reported. "I think it is impossible because it would be less than three weeks' training after a long period without doing anything".
Six individuals at Premier League clubs tested positive for coronavirus this week, including Burnley assistant boss Ian Woan and Watford player Adrian Mariappa. "I've listened to all the arguments, I've been in the meetings, I've talked to the medical advisers, and I would be comfortable to do so".
While the top tier is taking baby steps towards emulating the Bundesliga's return to action, leagues in France, Scotland and the Netherlands have been abandoned because of the pandemic.
"It is the first step and we have to be sure when we go to contact training we have completed those processes".
Yet Werner warns that it could be a while before Liverpool's Anfield Stadium is filled with fans.
Asked if the Premier League had an exact date for a return, Masters said the organisation had to be "flexible".