Baldock was reportedly found dead in his home swimming pool in Glyfada, aged just 31.
State TV ERT said the player was "at the bottom of the pool" and a bottle of alcohol was found at the scene.
ANA said Baldock's wife, who is abroad, alerted the owner of the residence after unsuccessfully trying to reach the player on the phone.
Police cars and an ambulance were outside the building and a coroner was called to examine the body, ERT said.
The defender left England in the summer of 2024 to join Panathinaikos in the Greek Super League after a highly successful seven-year stint with Sheffield United in both the Championship and Premier League.
In an official statement, the Greek Super League confirmed the death of the 31-year-old.
"The entire Super League football family expresses its deep sorrow for the untimely loss of Panathinaikos and our National Team footballer, George Baldock, and extends its deepest condolences to his family and loved ones."
After breaking into senior football with MK Dons, Baldock earned a move to Sheffield United in 2017 and was a key part of two separate promotion campaigns - while also featuring 38 times as the Blades recorded an impressive ninth-placed finish in England's top flight in 2020.
The defender was a fan favourite at Bramall Lane having made 219 appearances, registering six goals and 16 assists.
Sheffield United paid tribute to Baldock on social media: "Sheffield United Football Club is shocked and extremely saddened to learn of the passing of former player, George Baldock.
"The defender left the club in the summer after seven years at Bramall Lane and was extremely popular with supporters, staff and teammates who pulled on a red and white shirt alongside him.
"The sincere condolences of everyone associated with Sheffield United are extended to George's family and friends."
A 12-time Greece international, Baldock had featured on four occasions for Panathinaikos this season but had not been selected for the national team's Nations League match against England at Wembley on Thursday.
England's official X account also paid tribute to the defender ahead of their game against Greece.
"We're extremely saddened by the passing of George Baldock.
"George was close to many of our players, and represented Greece – our opponents on Thursday night.
"We're thinking of George's family, friends and teammates at club and country at this difficult time."
