The Argentine is being released at the end of this season and is being heavily linked with a move to the Blues.
Thomas Tuchel is in the market for a striker after Timo Werner ’s struggles in front of goal, with Aguero making a mouth-watering option.
But the 32-year-old should be warned, it does not always work out well for those who swap Premier League clubs to move to Stamford Bridge.
Here Mirror Football looks at five players whose time at Chelsea did not work out…
1. Juan Sebastian Veron, £14million from Manchester United
Veron’s Chelsea career started remarkably well, scoring a goal on his Premier League debut for the club against Liverpool.
But that was as good as it got for the Argentine, who would go on to make just six more appearances for the Blues in the top-flight.
The midfielder was hampered by injuries and when Jose Mourinho took over from Claudio Ranieri, Veron was sent out on loan to Inter Milan and never again played in the Premier League.
2. Fernando Torres, £50million from Liverpool
Torres remains one of the most expensive flops in Premier League history after joining the Blues from Liverpool in the January of 2011.
The Spanish striker went 903 minutes and nine games without scoring a goal in the top-flight as he struggled to adapt to life at Stamford Bridge.
The next season did not go any better for Torres, with his Chelsea career epitomised by a horrendous miss against Manchester United when he put the ball wide after rounding the keeper.
Despite starting the majority of Chelsea’s games during his time at the club, Torres’ troubles continued before he eventually departed to AC Milan.
3. Danny Drinkwater, £35million from Leicester City
It would be hard to find a player who has suffered a fall from grace that would rival Danny Drinkwater’s.
The midfielder arrived at Stamford Bridge as a Premier League winner but has never been able to nail down a place in the Chelsea squad.
Drinkwater’s nadir was undoubtedly Mauricio Sarri’s season in charge, when the Englishman made no league appearances whatsoever.
He has been sent out on loan to two Premier League clubs, both of which were failures and was not handed a squad number at the start of this season.
4. Shaun Wright-Phillips, £21million from Manchester City
The son of legendary Arsenal striker Ian Wright, the tricky winger was limited to only sporadic appearances at Chelsea.
Wright-Phillips was a perennial substitute under Jose Mourinho, coming off the bench 39 times in the Premier League during his time at the Blues.
It took him 17 months to score his first goal, but his lowest would be his final season at the club when he was left out of the squad completely for the 2008 Champions League final.
After Avram Grant left the club, Wright-Phillips fell out with new manager Luiz Filipe Scolari and was allowed to return to City for just £8.5m.
5. Ross Barkley, £15million from Everton
To call Barkley a flop might be slightly harsh, but he has certainly suffered a mixed career since joining Chelsea from Everton.
It did though take him nine months to score his first goal for the club and he has failed to nail down a starting spot at the Blues.
In fact, Barkley has been on the bench nearly 20 times more than he has started a match during his time at Chelsea and he was sent out on loan to Aston Villa for this season.
[email protected] (Jacob Leeks)
This article originally appeared on Mirror – Football