However, despite following the player, Sky also report that the Jose Mourinho's Blues are reluctant to pay Liverpool's £50 million asking price.
Chelsea famously paid the Reds a similar fee for Fernando Torres in 2011, only for the Spaniard to struggle during his time at Stamford Bridge.
Sterling is arguably England's most promising player considering his age, and with the value of homegrown players set to rise in coming years if rules about registering players are to change, it's no surprise to see Chelsea join Manchester City and Arsenal in their chase of the former QPR trainee, with Manchester United and Real Madrid also mentioned.
The former two especially have problems regarding homegrown players currently in or around the first eleven, and both will be eager to recruit the best young British players whenever they become available.
However, Sky also say that aside from City's £25 million offer, there has been no other bids made for the player.