As the oldest living state leaders seem to be a pretty strong group, here's a list of the top 5 (plus the two "unclear status" ones) a picture of the person is above his name.
(101th birthday, March 2021)
(Unclear status) - Josip Manolić (b. 22th of March 1920)
Second Prime Minister of Croatia 1990-1991. Croatia was still a part of SFR Yugoslavia until 1991. A meme in his country for how youthful he is. Seems to still be very healthy.
(100th birthday, January 2021)
1 - Mustafa Ben Halim (b. 29th January 1921)
Libyan Prime Minister 1954-1957. Only Kingdom of Libya leader who lived long enough to see Gaddafi fall.
(Unclear status) - Kim Yong-ju (b. September 1921?)
Vice President during Vacancy 1994-1998. Not much information on how he's doing nowadays or if he is even alive.
(2016)
2 - Francisco Morales-Bermúdez (b. 4th October 1921)
Military dictator/President of Peru 1975-1980. Sentenced to life imprisonment in Italy in 2017.
(16th of April 2021, vaccinated for COVID)
3 - Luis Echeverría (b. 17th January 1922)
Mexican President 1970-1976. Banned rock music recorded my Mexican bands in 1971. He was hospitalized in 2018, is now in a wheelchair.
(2016)
4 - Khamtai Siphandon (b. 8th February 1924)
First the Laotian Prime Minister 1991-1998, then the President 1998-2006. Stepped down in 2006, his predecessor as President (Nouhak Phoumsavanh) lived to 98. One of the more quiet people on this list.
(Late 2020)
5 - Tomiichi Murayama (b. 3rd March 1924)
Japanese Prime Minister 1994-1996 known for releasing the Murayama Statement. Still in good health.