The deal would make the Argentina striker the highest-paid player in the Barclays Premier League at more than £170,000-a-week.
Over the summer Chelsea had a £31m bid for Aguero turned down last summer but are now prepared to increase their offer after seeing Aguero score two stunning goals against Chelsea in the Champions League earlier this month.
The Argentina forward has a £53m buy-out clause in his contract but Chelsea believe they can land Aguero for less as he would be ineligible to play for them in the Champions League.
Aguero seems to have welcomed Chelsea’s approach saying:
“It’s nice people say I could play in a team like Chelsea. They are one of the best in the world. I like it (Chelsea’s interest) and it makes me happy.”
As to where Aguero would play, Chelsea boss Carlo Ancelotti said:
“I like him. I think Aguero can play with Drogba for sure.”