His future at the Etihad under Pep Guardiola was put in doubt earlier in the year after he lost his starting place to Gabriel Jesus.
It was reported during the 2016/17 campaign that Guardiola and Aguero did not have the best relationship, with the Spaniard apparently feeling the Argentine could have worked harder in City's attack.
Sources for Sky Sports claim that the Blues have a "strong and serious" interest in signing the Argentinian and is one of a number of options in this summer's transfer market.
Chelsea are in search of an elite striker having missed out on Romelu Lukaku to Manchester United recently, and have been linked with the likes of Álvaro Morata, Andrea Belotti and Pierre-Emerick Aubameyang since missing out on Lukaku.
The Blues are looking to replace Diego Costa this summer who, according to The Telegraph, is set to leave Chelsea for Atlético Madrid and the London club have identified the Premier League goal machine as an ideal replacement.
Manager Antonio Conte is still desperately searching for a world class striker and time is running out. "It has never been in doubt". We are a team that aspires to win every competition we compete in.
But it remains to be seen whether Manchester City would be prepared to sell the prolific striker to Premier League title rivals in the shape of Chelsea.
Aguero has been a superb signing for City since arriving from Atletico Madrid in 2011 and he still has three years left on his deal so the Citizens are under no pressure to cash-in.