The Football Association’s chief executive, Martin Glenn, has said he would love to see a Champions League spot for the winners of the FA Cup as part of wider talks that will explore axing replays and introducing a winter break.

Amid renewed determination from the FA, Premier League and Football League to address long-term issues surrounding fixture congestion, Glenn also revealed that they would join forces to take on Uefa over the creeping number of “blackout” dates as a result of European competition.

“When I talk about reform I think we have to reform together with the leagues and reform the fixture schedule period, for the good of English football,” Glenn said. “Lots of things have to give. This isn’t an FA Cup problem. That hasn’t changed – all the things around it have. We’re always open to evolve the competition, keep it relevant, make it attractive.”

He said that the FA, Premier League and Football League had recently completed four-year plans and agreed it would be sensible to take a strategic look at the fixture calendar. One aspect could be to explore again the idea of giving the FA Cup winners a Champions League slot, he said.

“Yeah, I’d love to see that,” he said. “It would add lustre to the competition. You can’t solve things in isolation. It’s a Rubik’s Cube. That might be one possibility Of course, running the FA, I’d love it.

“It just needs to be set up and weighed up against all the other criteria and the desires of the competition owners, the Premier League, the Football League, etc. I think it would be attractive but you’ve got job one [which] is make sure we’ve got enough coefficient points in Europe to make sure we keep the four places.”

Before a fifth-round weekend in which the issue of fixture congestion has again reared its head owing to the scheduling of Manchester City’s trip to Chelsea three days in advance of a crucial Champions League tie, Glenn said nothing was off the table. Alongside the possibility of axing FA Cup replays and two-leg League Cup semi-finals, another hardy perennial – reducing the Premier League to 18 teams – could be part of the blue-sky thinking exercise.

“If you wanted a winter break, things would have to change,” Glenn said at a Kick It Out fundraising event. “But it doesn’t automatically mean that the Premier League would have to come down to 18 clubs either. I think there are other ways of fixing it but it just needs a holistic look at the entire calendar. It needs challenging probably Uefa about windows, so we need a negotiating strategy for that.”

Besides a shared determination to challenge Uefa over the number of midweek dates reserved for its competitions, Glenn said there was a desire in English football to relieve the possible damage fixture pile-ups could do to the national side and the chances of English clubs in Europe.

“We’re all just saying the same things, which is: ‘This isn’t great where we’re kind of managing from hand to mouth. We should get round to looking at it.’ But it’s a long-term thing, not a short-term thing.”

There can be no changes to the FA Cup until after 2018, when the current TV deals come to an end, and any changes to Uefa’s rules that forbid fixtures being scheduled on the same night as Champions League or Europa League matches would take time to negotiate. In the past, prize money has been withheld from English clubs because the rules were flouted.

The possible introduction of a winter break appears more credible than at any time since the dawn of the Premier League in 1992, after Glenn said that although it was not yet official FA policy he thought there was “huge merit” in the idea.

“It’s not FA policy but I would love there to be a winter break,” he said. “I think it’d be good for the England team, I think it’d probably be good for the clubs. So, how might you design a season that looks like that?”

Historically, the Premier League has argued that FA Cup replays would have to go if a winter break were to be considered. Glenn said there were no active talks but that there was a shared will to take the issue forward.