"There are no problems between Mourinho and I," former Argentine international Valdano said at a club event when asked about reports on Wednesday that Mourinho was unhappy and thinking of leaving at the end of the season.
"He is our coach, the man who must lead us to triumph, and the team is proving to be very competitive under him."
It was the second time in less than a month Real had to deny reports about a rift involving the pair.
Valdano has a powerful position as president Florentino Perez's right-hand man while the outspoken Mourinho is someone who likes to have total control of his team and coaching staff.
The Portuguese told a news conference last month he had no personal problems with anyone at the club after complaining Real officials were not doing enough to support his criticism of referees he believed favoured opposing teams.
"I can deny the personal relationship (with Valdano) is bad," the former Inter Milan and Chelsea coach said at the time.
Asked about his relationship with Valdano after Real knocked city rivals Atletico out of the King's Cup and booked a place in the last four on Thursday, Mourinho replied: "No comment."
He added that he intended to stay until the end of the season and beyond "as long as everyone is happy".
Mourinho, who joined Real on a four-year contract at the end of last season, has also expressed frustration at the club's failure to find a replacement for injured striker Gonzalo Higuain who will be out for four months due to back surgery.
"We are working on signing a striker and may have definitive news on that subject this week," Valdano said on Thursday.
"It's all about being better each season and we are better now than we were in the previous campaign. We expect to keep this up."
Real are four points behind leaders Barcelona in La Liga and host Real Mallorca on Sunday.
