Premier League chief executive Richard Masters says there will be flexibility over the target resumption date of June 12.
A key step towards the return of England's top flight amid the coronavirus pandemic was made on Monday when clubs unanimously voted to approve training in small groups from Tuesday.
Despite reports about conflicts of interest among the 20 teams on various aspects of "Project Restart", a consensus was reached with regards to the first phase of resuming action.
Players will have to maintain social distancing during training sessions in small groups, while contact work is not yet allowed.
Masters explained the first batch of coronavirus test results should be in by 14:00 local time on Tuesday, after which training can begin.
He also addressed the targeted start date, insisting June 12 was not set in stone and concerns about whether players would be fit enough to play by then would be taken into account.
"Next week we are going to be discussing full contact training protocols," Masters said.
"Once you know when you can start full contact training, and we've had a proper discussion with clubs over how much is required to create the fitness levels before they can start playing, you're then in a position to confirm when the season start date is.
"We haven't changed the start date; we have to be flexible about it. What we don't want to do is continually move that start date.
"So, we haven't changed it but we need to be flexible and acknowledge we're in a step-by-step process.
"June 12 was a staging post; it wasn't a firm commitment. We know there's a discussion to be had, it really depends on when we can start full contact training.
"We have a process to go through before we can get to that stage."