"I spoke with the manager and we said that it doesn't make sense for me to go to the Olympics as I would miss the first two league games of the season and of course I want to play in them," Karius told the British media.
"We agreed together I wouldn't be going (to Rio). First I spoke with Jurgen and then together we spoke with the German people who wanted me to go.
"The priority is the club. It's more important that I am available for the start of the season."
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Mignolet, 28, joined the Merseyside club in 2013 and was handed a contract extension in January that would keep the Belgian international at Anfield until 2021.
"Of course I know that a club like this has more competition," Karius said. "It's a bigger club and better players means more competition.
"But I am not scared of anything. I'm not a keeper who hasn't shown his ability."
The 16-team Olympic football competition is restricted to under-23 players with only three overage players allowed. World champions Germany have been paired with 2012 Olympic gold medallist Mexico, South Korea and Fiji in Group C.
(Reporting by Ian Rodricks in Bengaluru; editing by Sudipto Ganguly)
