Football Association chief executive Martin Glenn is optimistic that English football can introduce a winter break but said it cannot be brought in until the Premier League TV deal expires in 2019.
There have been calls for many years for English football to follow in the footsteps of nations including Germany and Spain in providing clubs with a rest period in mid-season.
Many have suggested that England are at a disadvantage at major international tournaments due to fatigue as players face a 38-game Premier League season in addition to two domestic cups and the possibility of European competition.
Glenn said the FA, which has responsibility for the FA Cup as well as the England national team, supports the introduction of a break but that it cannot be implemented until the current Premier League TV rights deal expires at the end of the 2018-19 season.
"I can't make it happen," Glenn said. "To make it happen you need a whole-game solution. You need an agreement. The Football Association is a competition owner, as owner of the FA Cup, and the Premier League and English Football League need to agree too.
"There is a consensus that it would be a good thing to do. I'll say no more than that. We can do our bit about fixture congestion and that's why from the quarterfinals [of the FA Cup this season] we're not going to have replays.
"If we are going to get a winter break, which the FA very much wants, it would be after the current Premier League TV rights deal is done. There's more consensus for that than you might think.
"What scared people about winter breaks in the past is the thought of it being between Boxing Day and New Year but it doesn't have to be then. It can be after the FA Cup third round in mid-January.
"We can't do it on our own. We can do it collaboratively with the leagues but I think there is a growing consensus that it should happen."
Sam Allardyce, who has taken charge of England a decade after first being interviewed for the role, said he strongly favours the idea of a winter break.
"I've been an advocate of a mid-season break for about 10 years," he said. "The demand physically and mentally on the players is enormous.
"A break would help the players and would help the national team. January and February is always the most difficult period."