Wales' Aaron Ramsey
Ramsey was part of the Wales side that were knocked out of the tournament at the semi-finals by Portugal on Wednesday, while Özil was part of the Germany side that lost to France - with Giroud and Koscielny both playing a part for the host nation who will face Portugal in the final on Sunday.
Germany's Mesut Ozil reacts after the game
They report that they will show up to pre-season training just 13 days before their league campaign starts.
The Gunners, of course, aren't the only side likely to be without players. Liverpool could be without Emre Can, who was part of the Germany side, while Joe Allen and Danny Ward were members of the Wales squad - though only Can is likely to be pushing for a place in the starting XI come the opening day. They are all likely to miss the tour to the United States as part of their pre-season schedule - but games against Barcelona and Mainz could determine whether or not Jurgen Klopp feels they are in a good enough state to start the season.
Germany's Emre Can reacts
It will be interesting to see just how the European Championships affect both sides start to the new Premier League season, as both sides still have a number of players they can call upon to each put out a strong starting XI to get their campaigns underway.
France's Olivier Giroud reacts