Allardyce wants the chance for players to recharge their batteries during the season and Scudamore has held talks over a revamp of English football’s calendar that would include a rest period.
Any shake-up of the congested fixture list cannot be introduced until 2019 as only then is the new £5bn record TV deal completed.
But in the wake of new England boss Sam Allardyce leading the latest calls for a change to the season’s structure, Scudamore says discussions are on-going.
“He (Allardyce) has been very consistent and has been calling for it for a lot time, as has every England manager,” said Scudamore.
“There are more prospects for it than I can remember.
“We are having discussions but it’s not easy due to the calendar of different competitions.
“We are open-minded and keen if we can make it work. We all know what we have to do to create space and something has to give.
“It would have to be decided by the next TV market which is sometime at the end of 2017 and the start of 2018.”
Allardyce believes easing burnout fears would help England compete with the world’s best nations, including the likes of Spain and Germany who enjoy a post-Christmas breaks.
But Scudamore says the Premier League is not to blame for England’s latest failure at a major tournament.
The Three Lions suffered an embarrassing Euros elimination at the hands of Iceland at the last-16 stage.
Speaking at the launch of Premier League 2, a new ‘reserve’ division to replace the existing Under-21 set-up, Scudamore added: “We did our own post-Euros discussion and there is nothing we saw that put us off the journey.
“We saw nothing in the Euros, either from other teams or from ourselves, quite frankly, that said we have to change the journey.”