Benitez: Kyrgiakos will add strength & experience
Kyrgiakos, 30, who has 49 caps, is expected to complete his medical at the Premier League club on Friday.
"We have nearly done the deal subject to a medical. He is a player with experience who can hopefully help us in defence," Benitez told the Anfield team's website.
"He has experience in British football at Rangers. After that with (Eintracht) Frankfurt and the national team.
"He's a good player in the air, strong and aggressive. We were looking for a player with experience," added Benitez.
Kyrgiakos said Liverpool was a challenge he could not turn down.
"Last week I said I was an AEK player for the next four years and meant that," he said on his official website.
"But then I received the biggest challenge of my career. I fully understand it came at the worst possible moment for the team but the fact I had the chance to play for Liverpool is a huge challenge."