Pato has been strongly linked with a move to the Premier League.
The Brazilian striker appears to be available for £11 million, and interim manager Guus Hiddink has suggested that it could be an area of the team the Blues need to strengthen in.
However, the report does state that Chelsea have reservations about the signing the Brazilian, given his history.
Pato has been linked to other Premier League clubs, including Liverpool, but that was firmly denied in a press conference by their manager Jurgen Klopp.
The Blues currently have Diego Costa, Loic Remy and Radamel Falcao at their disposal, but all three of them have had their fair share of problems with injuries, especially Falcao, as the Colombian has been sidelined for some time.
Given the strong rumours that have been circulating about the Brazilian, it would appear that his days are numbered at his current club, and that his representatives are actively seeking a good move for the 26-year-old.
The former AC Milan forward scored 63 goals in 150 games during his time with the Italian giants, and since he left the Serie A side to return to his home country, he has continued to average around one goal in three games. He has recently been spending time on loan from Corinthians at Sao Paulo - and has actually made more appearances for the latter of the two.
Whether Chelsea feel that is good enough for them remains to be seen, but they will want a striker of top quality to come in to rebuild themselves ahead of next season.