Costa appears close to a £35 million switch to Stamford Bridge, but with Samuel Eto'o leaving and doubts over Fernando Torres and Demba Ba they are likely to need further reinforcements this summer.
According to the Daily Star, Mourinho has narrowed down his options to three players - Bony, Remy or Lukaku.
Remy is believed to be available for around £8 million from QPR, but both Arsenal and Tottenham are said to be interested so Chelsea will need to act quickly. Bony, who enjoyed a stellar campaign with Swansea is also believed to be on the Blues' radar - however the Welsh club's £25 million asking price could prove to be too much.
That leaves Lukaku, who appears to share something of a fractious relationship with the Special One.
The Belgian youngster impressed while on loan with Everton last year, however recent reports have suggested that Chelsea could be willing to sell for around £25 million.