The Brazilian-born striker is thought to be the London club’s principal target.
After previous attempts to sign Suárez, Rooney and Higuaín proved too difficult, Chelsea manager José Mourinho is firmly focussing his sights on Atlético Madrid talisman Diego Costa.
According to the English paper the Metro, Fernando Torres may be involved in the deal.
The London club previously tried to sign the naturalised Spaniard in January and now they are thought to be considering making a £20m offer and offering Torres as part of the deal.
According to the source, Chelsea hope to finalise a deal soon after the end of the current season to avoid paying a higher price if the player was to perform at the World Cup.
