The Premier League is “as confident as we can be” about restarting in June, says chief executive Richard Masters.
Players resumed training on Tuesday, the day it was announced there had been six positive tests for coronavirus across three clubs.
The Premier League, suspended on 13 March, had previously identified 12 June as a possible restart date.
“There is some momentum. We’ve taken the first step,” Masters told BBC Sport.
“It’s great for everybody, including the fans, to see our players back on the training ground.”
Asked what date the Premier League was targeting for a return, Masters said it must be “flexible” and could learn from the resumption of the Bundesliga last weekend.
He also recognised the need for “contingency plans” and said “curtailment is still a possibility”, meaning the season would be ended, but there was “optimism” fans could attend matches next season.
Masters also admitted the idea of scrapping relegation “would come up for discussion” and was “a significant topic”.
“That will be part of the debate we have,” he said. “What would happen in that environment (curtailment of season) is something we’re yet to discuss with the clubs.”
Football Association Chairman Greg Clarke told the Premier League clubs at their last meeting that the governing body would oppose the scrapping of relegation.
“I can’t speak for the FA but obviously they have their own views on it and until we’ve discussed it as clubs and as a collective we can’t really talk further about it,” Masters added.
Phase one of the return to training features small groups training with social distancing maintained.
On Wednesday culture secretary Oliver Dowden said phase two – the return of contact training in elite sports – could get government approval “later this week”.
Masters said the Premier League would not take this next step until it was safe to do so.
“We wouldn’t have taken the first step to get back to training if we weren’t convinced we had created a very safe environment for our players,” he said.
“It is the first step and we have to be sure when we go to contact training we have completed those processes.”
‘We think it is safe to return’
The Premier League hosted video conference calls “to provide health reassurances” to club captains and managers before training recommenced.
The league began testing players and staff for coronavirus again on Friday after six tested positive on Tuesday, a result Masters was “reassured by” given it represented less than 1% of tests.
“Our sympathies are with everybody who has tested positive,” he said. “A few of them were surprised because they were asymptomatic.”
Earlier this month, a number of club doctors raised concerns with league bosses over plans to resume the season and Masters said the Premier League “were very surprised to hear that”.
“We ran a very thorough consultation with club doctors,” he added.
“We have done everything we possibly can to make return to training as safe as possible.
“We think it is safe to return. We have to respect players’ decisions not to return to training. I would be comfortable to return to training.”
Should matches resume and Liverpool – 25 points clear at the top of the table – secure their first title in 30 years, Masters said they should be allowed a trophy presentation “if we can find a way of doing it”.
But some people are worried about fans gathering outside Anfield, and Masters said the potential for crowds of supporters was “a concern”.
Masters said the Premier League wanted “to play out the season as much as possible at home and away venues”.
“We’re talking to the authorities about that,” he added.
“I do believe we can appeal to fans not to congregate outside football grounds or go to other people’s houses to watch football matches in contravention of government guidelines.”