The former Greece international, 32 next month, originally joined on a two-year deal from AEK Athens at the start of the 2009-10 season.
Sign on: Kyrgiakos (right) has agreed a new one-year deal to remain at Anfield
However, written into that agreement was an option for a further year and Kyrgiakos has qualified for that having played the required number of matches last season.
Kyrgiakos was fourth in the pecking order of centre-backs in the previous campaign, behind Jamie Carragher, Martin Skrtel and Daniel Agger.
New recruits? Liverpool have been linked with moves for Dann (left) and Cahill
With the club looking to reinforce that area this summer his chances could be even more limited with Dalglish being linked with Birmingham centre-half Scott Dann and Bolton's Gary Cahill.
Liverpool have, however, confirmed the departure of a number of reserves with former captain Steve Irwin, Nikola Saric, Jason Banton, Deale Chamberlain, Alex Cooper and Sean Highdale all leaving.
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Explore more:People: Jamie Carragher, Scott Dann, Daniel Agger, Gary Cahill, Martin Skrtel Places: Birmingham, Liverpool, Greece