Peterborough director of football Barry Fry has revealed their interest in Edwards, who piqued their interest during trips to watch loanee Lucas Bergstrom.
“I've had conversations with people at Chelsea who are in the know and who would be involved in any decision-making," Fry told Peterborough Today.
“They came to watch Lucas, but they were taken by Ronnie. They haven't made a bid yet, but there are three weeks until the transfer window closes. They certainly like him.
“Virtually the entire Premier League know about Ronnie and it's interesting to see members of his England Under 19 team attracting attention now."