September or October had previously been mooted as possible return dates but Maxwell is more optimistic.
"I think it is likely that we will see football in August," he said. "We are seeing it in countries across Europe.
"I think it is definitely achievable, the plans we are putting in place are comprehensive. We have to make sure we are giving government comfort that we can do it in a manner that keeps the players, the staff, everybody involved in the game safe, and I'm sure we can do that."
But national clinical director Jason Leitch warned that professional sport would have to go through a number of stages before a return to competitive action.
Leitch said no dates had been attached to the phases.