As is a usual practice in Croatia, the statement did not name Lovren but said it charged a 29-year-old Croatian citizen,
citing details from his testimony given a year ago.
Croatian media, including the state television website, reported that Lovren was charged.
Lovren denied any wrongdoing in a post on his Instagram profile.
"I want to tell everyone that I'm innocent. I did not commit any criminal offense. I'm proud of my life, of what my family and I have achieved... I reject all accusations with indignation. I will win this battle," Lovren said.
In March this year, the state attorney also charged another Croatia international, Real Madrid midfielder Luka Modric, for false testimony in the same case.
Lovren testified at the trial of a tax official and three former senior officials from the soccer club Dinamo Zagreb, including its former chief executive Zdravko Mamic, about the dates of signing the annexes to his professional contracts which regulated transfer fees.
The Dinamo officials were charged with avoiding paying 12.2 million kuna ($1.92 million) in taxes and diverting 116 million kuna from the soccer club.. All of them denied any wrongdoing.
Lovren moved to Lyon from Dinamo Zagreb in 2010 and then joined Southampton in 2013 and Liverpool a year later. He and Modric both played in the Croatia team that was defeated 4-2 by France in the 2018 World Cup final.
A conviction for false testimony brings a jail term of between six months and five years.
Former Dinamo boss Zdravko Mamic fled to neighbouring Bosnia earlier this year briefly before being sentenced to prison in Croatia.
($1 = 6.3620 kuna)
(Reporting by Igor Ilic; Editing by Angus MacSwan and Pritha Sarkar)
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