Mourinho has made it clear he will improve his misfiring strikeforce after criticising Fernando Torres, Samuel Eto'o and Demba Ba at various times this season for not scoring enough Premier League goals.
The Blues have been linked with plenty of high-profile forwards over the past six months but the latest reports suggest Liverpool ace Suarez, Atletico Madrid's Costa and Paris Saint-Germain's Cavani are all under consideration.
Getting any of those players, however, is a different matter. Suarez has committed his future to the Reds by signing a new deal and is likely to stay if they manage to get back into the Champions League, while Costa is not thought to be in any hurry to leave Atletico with his side in with a great chance of winning La Liga this season.
However, offering former Atletico hero Torres as part of a swap deal may increase the chances of a transfer going through and Costa has been linked with a move to the Premier League over the past couple of years.
Cavani could be a more realistic option but would cost Chelsea in the region of £50m, while another name in the frame is thought to be Bayern Munich's Mario Mandzukic as Mourinho narrows down his summer options.