Both Premier League giants have been tracking the Nigerian winger in Millwall’s Under-16s and have made a move to land him.
Edozie has also featured in the U18s and U19s sides for the Lions this term despite his tender age.
He is one of the Championship club’s leading prospects with both City and Chelsea watching him in action.
But the Londoners are thought to be desperate to keep hold of their prodigy in order for him to continue his development.
City could pay as much as £1million to Millwall for Edozie.
His signing will be the second time the Pep Guardiola’s side have raided Millwall for one of their top young prospects.
Elsewhere, Newport County have signed goalkeeper Tom King from Millwall.
King, a former England Under-16 and 17 international, has signed a two year deal with the beaten League Two play-off finalists.
“I’m absolutely delighted to be joining Newport County, it’s a great chance for me to showcase my ability in an already flourishing team,” he explained.
“I am thrilled to welcome Tom to the club. He has good experience at this level,” boss Michael Flynn added.
“Tom reminds me of Joe Day when he first came to the club, he is a very talented goalkeeper and I look forward to working with him.”
Tom made 16 appearances for AFC Wimbledon last season.