The Spanish striker is on an extended holiday in Brazil after being exiled from the club following a public bust-up with manager Antonio Conte.
The club has been monitoring his antics on social media and are concerned that his pre-season indulgence is becoming all too visible, reports The Sun.
Chelsea are said to be keen to find a buyer for Costa as soon as possible after his proposed move to the Chinese Super League collapsed during the winter window.
The player's former employers Atletico Madrid have also been linked with a summer bid, but talks have reportedly broken down.
Costa is alleged to have opened legal proceedings against the Premier League champions for "blocking" his proposed move to Atletico.