Canadian receiver Chase Claypool impressed NFL scouts at the league's combine in February and its translated into draft hype which could result in a first round selection.
According to the ESPN report, GMs were concerned that there wouldn't be time for player physicals, psychological tests and other necessary player-vetting procedures.
The New York Giants and the New York Jets, for example, would not be able to access their buildings during draft night, as New Jersey is now under lockdown.
The reasoning behind the push to move the draft back is because the general managers don't feel they are getting adequate time to properly vet this year's draft prospects because much of the country is on lockdown because of the coronavirus outbreak.
In an internal email sent to all National Football League employees last Thursday, commissioner Roger Goodell hinted that some changes were coming to this year's event. The draft is still expected to be televised.
"The challenges we face are not unique", Goodell said in the letter.
Commissioner Roger Goodell issued a memo to clubs Tuesday outlining the new rules put in place to ensure the league "continues to conduct itself in a responsible way", and that teams "operate on a level playing field". The NFL said last week that it is exploring "innovative options for how the process will be conducted and will provide that information as it becomes available", via NFL.com's Dan Parr.
All NFL facilities will soon be closed to personnel - with some limited exceptions - in response to the coronavirus pandemic.
At least 18,900 people have died globally, with more than 422,780 confirmed cases.