The Croatia defender completed his protracted move from Southampton to Anfield on Sunday, signing a long-term deal with the club for an undisclosed fee.
With Brendan Rodgers and the first-team squad in the USA for the International Champions Cup, Lovren had been expected to fly out and possibly make his first appearance in Wednesday's match with Manchester City in New York.
However, the 25-year-old has revealed he will not feature in any of the games in America after being unable to get a visa, meaning he will have to wait until the week before the Premier League season begins to make his bow against Borussia Dortmund.
"Unfortunately, I could not immediately get a visa," he told Croatian newspaper Sportske Novosti. "Therefore I cannot join my new team-mates in the United States.
"I'm very sorry about that.
"Of course it's not good that I have not joined the team's preparations, however, I have plenty of days until their return from the tour.
"I will train with the Under-21 team in Liverpool, Brendan Rodgers will send me a programme for me to practice."
Lovren is one of six new signings to arrive at Liverpool during the close-season, with former Southampton team-mates Adam Lallana and Rickie Lambert now also part of Rodgers' squad.
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