Real Madrid are on the hunt for a new striker to replace injured Argentine Gonzalo Higuain, who could be out for four months.
Mourinho told a news conference he had spoken about the need for a new striker in November when it was obvious that Higuain would not be fit in time, according to the online site of sports daily Marca.
"I did not speak about it again," the Portuguese coach said.
"I am not the one sending messages," he added. "I got where I am thinking with my own head and I am too old for messages in the newspapers. Little messages don't get to me."
Real Madrid general manager Jorge Valdano spoke to the press after Madrid's shock 1-1 draw against bottom club Almeria on Sunday, saying Benzema was suffering "a great injustice."
"He is judged very time he is in contact with the ball. I think he is an excellent player, who knows how to play football and because of his youth we have great hopes," he reportedly said.
"Today we had a number nine on the bench," Valdano told the television station Canal Plus.
In an interview with Marca published Wednesday, Real Madrid striker Cristiano Ronaldo also rejected as unfair criticism that Benzema had failed to take advantage of the absence of Higuain.
"My sincere opinion is that Benzema does not deserve the things they are saying about him. If you analyse his last games you can see that he is making an effort, he is fighting. Sometimes things don't work out, just like goals, but Karim has enormous footballing value."
Benzema has had an unhappy time at Real since his multi-million euros move from French side Lyon in the summer of 2009, with his lack of form last season seeing him miss out on a place in the French squad for last year's World Cup finals.