It has been reported that the Blues had a £50m bid rejected for the Argentina international and are preparing a second offer.
But Mourinho says there was no such bid and said: "Nothing is true. He is a player that I know we cannot get.
"He moved from Real Madrid to Napoli six months ago and he's doing very well, he's adapting very well to Italy.
"Napoli is a club which normally doesn't sell. In the last years, they sold one player a year, when they felt it was not possible to keep them.
"They want to win the Scudetto, they want to win the Europa League. I don't believe they're interested in selling Higuain.
"Why should we be interested in someone we believe it is impossible to get?"
Chelsea are believed to be eager to augment their striking options due to the lack of goals being provided by Fernando Torres, Samuel Eto'o and Demba Ba.
But, when asked about the possibility of acquiring a new striker, Mourinho said: "It's not a priority, it's not an option. We have three.
"This squad is good enough for my first season, and for the objectives of the first season.
"We're building a new team. I think the fans trust the club, I think they trust me, and they know we're building a team for another period of seven, eight years."
Mourinho also reiterated his desire to keep attacking midfielder Juan Mata, who reacted angrily when substituted on New Year's Day and has been linked with a move away from Stamford Bridge during the transfer window.
Mourinho said: "He trained today in a fantastic way.
"I think he is focused on what I said after the game at Southampton, when I said 'I don't want him to leave'.
"I think he is focused on that and not on when I said 'the door is always open'.
"He trained in a fantastic way and so there are no problems."
Asked whether he would consider selling Mata to a Premier League club, Mourinho added: "No, I keep saying that I want him to stay.
"There are no offers for him."
However, Mourinho confirmed there has been interest in Kevin de Bruyne, amid reports the Belgian winger wants to leave in the transfer window.
Mourinho said: "This is the period for agents to be famous.
"We know Kevin didn't adapt very well to the difficult life a Chelsea player has, which is to pay a big price to play.
"They have to give a lot, to work a lot, and to accept competitiveness. This is the first time he came to a big club with big competition.
"He is a fantastic player with fantastic potential. I don't want him to leave but we have a couple of contacts made by other clubs.
"But, if people think they can get our good players on sale, the sales finished in London yesterday."