Blues boss Luiz Felipe Scolari is desperate to strengthen his strikeforce when the transfer windows opens in January and could make a move for the Brazilian striker.
Scolari was close to making a move for Fabiano when Didier Drogba almost joined Serie A side AC Milan in the summer.
It is believed Chelsea will be forced to pay more than his £12 million buyout clause should they make a move for the 27-year-old.
Fabiano signed a new deal with Sevilla last summer.
