Arsenal, Tottenham Hotspur and Everton are all in the running to finish seventh this season, going in the final day of the Premier League.
West Ham United need just a point from their last game against Southampton to seal a sixth-placed finish, which would see them qualify for next season's Europa League.
Tottenham, Everton and Arsenal are separated by just one point and whoever finishes seventh will enter the new Europa Conference League.
However, whichever team qualifies for UEFA's new tournament will face a packed early season schedule, with two extra games needing to be played during the opening 14 days of the new campaign.
Their involvement in the competition will start during the play-off round, with the first leg due to be played on August 19 and the second leg on August 26.
The new Premier League season is set to begin on August 14, meaning players who will have had a shorter off-season and pre-season because of the Euros face a packed start to the campaign, with four games in their first two weeks back.
When asked about the prospect of playing in the Conference League, Gunners boss Mikel Arteta said: "It's a new competition, so I don't really know what will happen.
"First of all, let's try to finish as high as possible and then we will determine, if we are involved, the best way is to do it.
"We have experienced in the last few years how tough it is being in the Europa League, given the amount of games you play and the short turnaround before Premier League matches.
"I think there is a lot of history there with teams that have been involved in the Europa League, and the negative consequences it has on the Premier League positions.
"We've tried to give it the best possible go, we came up a little bit short, but this club has to be in Europe."
Meanwhile, Everton boss Carlo Ancelotti said: "It is a different competition, it is a new competition. I think there were three competitions in Europe and then they changed and now another competition is back.
"It is not the most the exciting competition in Europe, we know. But participating could be good for us, for our future and the future of this club."
