Trouble flared at the Crown Social Club in Kingstanding, Birmingham, following England's penalty shoot-out defeat in July.
Disorder spilled out onto the street and injuries included a dislocated knee, broken eye socket and a broken nose.
Police have now released an image of a man they want to speak to about the trouble.
A West Midlands Police statement said: "We’re appealing for information following violence and disorder in Kingstanding after the Euro 2020 final.
"After the match on Sunday, 11 July, we were called to the Crown Social Club where more than 100 people had been watching the game.
"Lots of people were involved in arguing, fighting and disorder which spilled out into the street. Several people received serious injuries including a dislocated knee, broken eye socket and a broken nose.
"We’ve released an image of a man we would like to speak to about what happened. We also need help from people who were there on the night – if know something that might be able to help our investigation, please get in touch.
"If you can identify the person in the image that’s been released today, or if you have any other information, the easiest way to contact us is via Live Chat at west-midlands.police.uk or call 101 anytime.
"To remain 100 per cent anonymous please call Crimestoppers on 0800 555 111. Please quote log number 4052 of 11/07/21."