Hudson-Odoi was unhappy at a lack of playing time under previous Blues boss Maurizio Sarri.
Bayern were offering big money for a January transfer, but Chelsea refused to entertain any bids for the player.
He has since committed to the club by signing a new contract.
Green spoke to BBC 5 Live about the situation, saying: "We would hear the Bayern Munich chat, the chat about other clubs and Callum would just be there smiling.
"He knew it was all going on but it was water off a duck's back for him.
"Pressure didn't exist for him. It still doesn't.
"You look at someone like that, the way he carried himself, the confidence that he had in and around the dressing room was incredible to watch."