Mourinho complained at the weekend that the club were not doing enough to support his criticism of referees he believed favoured opposing sides and Spanish media later said he and Valdano were at loggerheads over the issue.
"I can deny that the personal relationship is bad," the flamboyant Portuguese told a news conference after Real's 8-0 King's Cup thumping of Levante on Wednesday when asked about Valdano.
"I have no personal problems with anyone," he added. "That's the most important thing."
Speaking in an earlier television interview, Valdano said the media reaction to Mourinho's comments about referees had been exaggerated and it was "a small thing".
"We all have a certain type of personality and you have to accept that," the Argentine added.
"We have a great team with a great future and a very, very competent coach and that should be enough to keep all the Madrid family happy."
Mourinho, who joined Real from Inter Milan at the end of last season, said it was normal for professionals working together in a high-pressure environment to have "differences of opinion" and he welcomed criticism.
"I have never been a 'yes man'," he said.
"I like criticism, whether I make it or someone else. But I repeat. Personal problems? Zero.
"That for me is fundamental because the day I have personal problems I'll be out shortly after."
The former Chelsea manager said he had left the Premier League club because of the arrival of two people, whom he did not identify, who were brought in during his fourth season at Stamford Bridge.
"Two people arrived at the club with whom I had no personal relationship and a few months later, I was out.
"My intention at Real Madrid is to see out the four years of my contract."
