Nineteen games have been postponed across the EFL this weekend.
It means more than half of the games in the Championship, League One and League Two will not take place this weekend.
"If we think a circuit breaker will help we will do it but, at the moment, there’s no scientific evidence to suggest that it will help," Parry told BBC Football Focus.
"We’ve got to stick together, stay calm and keep making balanced decisions on the basis of the latest information.
"We wondered if a short sharp circuit breaker this weekend would help but, frankly, it wouldn’t.
"There is no science to suggest it would help and, if you look at the geographical spread, there are areas where games can go ahead and where they can’t.
"There’s talk of the government having a two-week lockdown after Christmas so maybe that will be taken out of our hands.
"We are getting more information listening to the scientists, they need more data to try to work out exactly where we are going with this new strain. It is too early to tell.
"Next week we might be in a different position."