Madrid have earmarked the 24-year-old Wales international as their major summer target but have so far not persuaded Spurs to sell.
Madrid-based newspaper Marca's front page on Tuesday morning suggested Spurs were holding out for a fee of 145 million euros (£126million), which would far exceed the world record £80million the club shelled out on Cristiano Ronaldo in 2009.
Whether president Florentino Perez is willing to go to those lengths remains to be seen but Casillas, speaking on the club's tour of the United States, said: "We are talking about one of the top three or four best players in Europe and it's normal that his name is being discussed because he has all the qualities a footballer needs.
"Every transfer is controversial in its own way, for better or worse, but we are speaking about a very good, decisive player.
"I'm sure we'll make another signing before the transfer window shuts."
Casillas also gave his seal of approval to new Madrid boss Carlo Ancelotti, who took over from Jose Mourinho last month.
"I had the chance to meet Ancelotti during the summer holidays in Madrid and I'm excited about working with him," said Casillas, who hopes the Italian can right the wrongs of last season's trophyless campaign.
"I spoke to him for just five minutes and I came to the conclusion he is a winner. He makes that clear to you from the start.
"Whenever a new coach comes in it's a new challenge and I'm happy about starting a new era.
"Madrid need to start winning games and trophies after last season and fight for all three competitions."
Casillas spent the latter half of last season on the sidelines after injuring his hand and then slipping below Diego Lopez in the pecking order.
He declared his determination to get back in the first team next season, but insisted he was not taking his place in the side for granted.
"I have to compete. I would love to play, but I have to start from scratch. I am very excited now I am here, but my team-mates aren't going to make it easy for me," he added.
"It's good there is competition, because the coach and the whole team benefit from that. But there is a lot of competition for every position and my aim is to get back to my best and compete."