The 29-year-old will leave Hearts as a free agent in January, according to his agent.
“It’s not easy for him, as he’s not in the team and hasn’t had a chance this year,” agent Alexander Szatmari told the Daily Record.
“He feels a change is necessary and I will now try to find a new club.”
Balogh joined Hearts from Debrecen in February 2009 after an initial loan spell at the club.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.