Citing sources, Sky Sports says the Blues have "serious and strong interest" in Aguero, although City have no intention of letting the Argentina international leave the Etihad Stadium.
Romelu Lukaku was reported to be Chelsea boss Antonio Conte's priority target, but the Belgian snubbed the Premier League champions to agree a £75m ($98m) move to Manchester United from Everton earlier this month.
The setback prompted Conte to expand his search for a top-class striker, with Real Madrid forward Alvaro Morata, Borussia Dortmund striker Pierre-Emerick Aubameyang, Juventus striker Gonzalo Higuain and Torino's Andrea Belotti among the names being linked with a move to Stamford Bridge.
Costa is expected to leave Chelsea this summer after the Spain striker was told by Conte that he was no longer part of his plans.
The 28-year-old is yet to return to pre-season training at Chelsea and has been left out of the Blues squad travelling to the Far East for a pre-season tour.
Aguero joined City from Atletico Madrid in 2011 for a fee in the region of £35m and is the highest South American scorer in the history of the Premier League.
City chairman Khaldoon Al Mubarak dismissed speculation linking Aguero with a move away from the Etihad in May.
"I've read a lot about the speculation on this and it is ridiculous," he was quoted as saying by Eurosport.
"Sergio Aguero is one of the best players in the world and we are a team that aspires to win in every competition we compete in.
"Having Sergio Aguero as part of the squad is an absolute must and has never been a doubt."
City manager Pep Guardiola also ruled out Aguero being sold in the summer after the club's final league game of the 2016/17 season against Watford.
"He will be here next season. Happy? Good. Perfect," the Spaniard was reported as saying by the Daily Mail.