The Argentine forward announced on social media that he would be ending his ten-year stint at the Etihad Stadium at the end of the season after failing to reach an agreement with City over a new contract.
The 32-year-old striker will be available on a free transfer next season and has generated interest from the likes of Paris Saint-Germain and Barcelona. However, the Standard reports that Aguero is keen to stay in England to break the all-time scoring record in the Premier League.
Chelsea manager Thomas Tuchel and club executive Marina Granovskaia are both said to be interested in the move as they look to bolster the attacking options at Stamford Bridge.
The Blues have struggled to create clear-cut chances and goals this season despite having the likes of Timo Werner, Kai Havertz, Olivier Giroud, and Tammy Abraham in their squad. Chelsea have also been heavily linked with a move for Borussia Dortmund's Erling Haaland - one of the world's most sought-after players.
Chelsea handed boost as Man City boss Pep Guardiola plays down links with Erling Haaland
With Manchester City all set to lose Sergio Aguero at the end of the season, Pep Guardiola's side has been rumoured to be in the market for a new centre-forward, with Erling Haaland reportedly at the top of the list.
However, prior to Manchester City's Premier League encounter against Leicester City last week, the Spanish manager played down the possibility of signing a big-money striker this summer.
"With these prices, we are not going to buy any striker," Guardiola said. "It is impossible, we cannot afford it. All the clubs struggle financially and we are not an exception."
"We have Gabriel [Jesus], Ferran [Torres] and a lot of players in the academy and we sometimes play with a false nine. There is a big chance that we are not going to sign a new striker for next season," added Guardiola.
Following Guardiola's comments, Chelsea could possibly be the only Premier League side vying for the player's signature. Reports suggest that Manchester United have prioritised a move for a centre-back and right-winger over signing the 20-year-old.
However, the Blues will have to break the bank to secure the Norwegian striker's services next season. They will also face competition from Real Madrid and Barcelona. Haaland's agent Mino Raiola, along with the player's father, have reportedly already met with representatives of both the Spanish giants.