Higuain is out for the season due to back surgery.
When asked if he still had hope Madrid would sign a centre forward this month, Mourinho said: "Not much. I spoke with the president a couple of days ago and nothing.
"My relationship with him is very good and I hope that it will be like that until the end, or even better. It's always been like that with my presidents.
"But at this moment, after the investments that the club have made in the last two years, the club aren't keen on signing another striker.
"Also, because this is Madrid, you cannot just sign any player and to me it doesn't seem a very easy situation.
"I have to try and get the best of the players that I have, who are numerous and very good.
"I only have one centre-forward, who is Benzema, but we need to face up to the situation in front of us.
"I suppose that until the end of January we will continue talking about this because the window is open until the end of the month, but I think that this is the group of players that I will have until the end of the season."