Panzo's Chelsea scholarship expires in 2019, and he has informed Stamford Bridge officials that he wants to move to the Ligue 1 club.
The Blues will be due a fee if the deal for the 17-year-old is completed, reported to be £2.5 million (€2.8m/$3.3m).
Michael Emenalo, formerly the Premier League club's technical director, has played a pivotal role in convincing Panzo to join Monaco, with the England Under-17 centre-back thus becoming the latest British player to try his luck abroad.
He will be the second Blues youngster to leave for an overseas club in recent months, with Harvey St Clair having joined Venezia in Italy's Serie B.
Callum Hudson-Odoi, who broke into the first team under Antonio Conte last season, also has several European clubs interested in securing his services, as top clubs including the likes of Barcelona, Real Madrid and Bayern Munich keep tabs on his development.
Panzo won the Under-17 World Cup with England last year, and has also been capped at Under-18 level.
He enjoyed a stellar 2017-18 campaign, making 21 appearances in all competitions, with the club winning an unprecedented quadruple of the U18 Premier League southern title, U18 Premier League Cup, FA Youth Cup and the U18 Premier League.
Elsewhere, Trevoh Chalobah's loan move to Ipswich Town is close to being finalised. He was close to following his brother Nathaniel out of the door at Stamford Bridge but received assurances from the club and signed a new three-and-a-half year deal in March.