Mourinho spoke at Friday's press conference, from which the club's official Twitter account reported:
Napoli have not given any encouragement to Chelsea in their efforts to land Higuaín and insist the Argentine, who played under Mourinho at Real Madrid, is not for sale.
That may not deter Chelsea owner Roman Abramovich, who agrees the lack of goals from strikers is the major weakness in the side.
He is willing to back Mourinho in the transfer market, even though the club posted losses of almost £50 million last season.
Stamford Bridge could be the scene of major upheaval during the January transfer window with Juan Mata, Kevin de Bruyne and Demba Ba all linked with moves away from Chelsea as Mourinho looks at ways to fund the purchase of a new striker.
Mata is the subject of interest from Paris Saint-Germain and Napoli, per Mark Irwin and Andrew Dillon of the Sun, De Bruyne could make a return to the Bundesliga, according to Matt Law in the Telegraph, while Ba is reportedly interesting West Ham, per James Dickenson at the Express.
However, Mourinho doesn't expect individuals to leave:
It is Mourinho's need for a new striker that will be key to the club's hopes of winning the Premier League for the first time since 2009-10.
Between them the club's current striking options, Fernando Torres, Samuel Eto'o and Ba, have only scored seven league goals this season.
Mourinho has previously been coy about his plans to add reinforcements to his attack, as reported by ESPN, but he will surely be assessing his options—regardless of what he says publicly.
Higuain's record of nine goals in 16 games since signing for Napoli is commendable but a striker with his attributes is not what Chelsea need, they already have Torres and Eto'o capable of filling that role.
Although he didn't figure in Mourinho's plans for the Blues at the beginning of the season, Lukaku's form at Everton—eight goals in 18 games—has illustrated that he is capable of making the grade.
Lukaku's ability to bring players like Eden Hazard, Oscar and Willian into play would benefit Chelsea's style and give the club the forceful all-round attacking figure they have lacked since the departure of Didier Drogba.