Mourinho has barely concealed his contempt for Valdano, who is number two to president Florentino Perez, and pointedly told reporters last week he does not speak to the Argentine about player transfers.
"The most important thing, from my responsibility, is to avoid creating more tension," Valdano said after Real won 1-0 at Sevilla in their King's Cup semi-final first leg on Wednesday.
"We have to see in what way the coach can feel more comfortable," he added.
"We are working to create the necessary conditions for the coach to act autonomously."
The outspoken Mourinho has complained of a lack of support from club officials over his criticism of referees and was unhappy that Real initially appeared reluctant to bring in a striker to replace the injured Gonzalo Higuain.
The former Inter Milan and Chelsea manager's request was granted this week when Real signed Emmanuel Adebayor from Manchester City on loan until the end of the season.
Valdano has insisted all is well between him and Mourinho, but acknowledged the coach may need to be given more space.
"If it is necessary to keep distance, distance will be kept," he said.
"The enemies are our opponents and often they are very fierce. That's where we have to focus our energies so we can put in great performances like the one today."
