The 23-year-old old attacking midfielder enjoyed a stellar World Cup as his side reached the quarter-finals, claiming the Golden Boot and earning a move to the Spanish capital in the process.
The European champions have also been linked with a move for Falcao, whom James played alongside at both Monaco and Porto, and the young playmaker hopes to be reunited with the former Atletico Madrid forward before the start of the new season.
"I'm sure he can play here," James told AS. "But I'm not the one who decides whether or not he goes. It's up to the president (Florentino Perez).
"But he could come here because he was the quality and attitude of a winner.
"I've played with him for four years, we were only apart when he left for Atletico. He has a winning mentality and that's what he had at Madrid. Hopefully he comes here."
James joined Madrid for a sum of €80 million but the 23-year-old is not taking his place in Carlo Ancelotti's first XI for granted.
"First, I have to train well to be among the XI," he insisted. "Almost all of the others have been together for three or four years.
"I have to respect them and come in little by little and when I get opportunities, show a high level. I'm happy because a dream is being fulfilled.
"Hopefully, everything goes well, I'm very excited and looking forward. I want to win titles with this great club.
"Since I found out that Madrid wanted me, I did everything in my power to go. It's big and it means that you have to be at a very high level."
James also admitted that he was not happy with the added media attention that has been forced upon him since his move to the Bernabeu.
"I don't like it at all," he confessed. "Leaving home and having the cameras all over you ... There's nothing better than going out and being calm. But I'm not at a point where I can do that.
"I understand and know how to handle it. I'm at a big club for the media."
Finally, Falcao urged his Colombia team-mates to try to persuade coach Jose Pekerman to remain in charge of the national team, despite reported interest from the Argentine FA.
"We all have to force Jose to stay," he declared. "He changed everything in our team for the better. He made good changes.
"If he doesn't continue, it will be sad and there will be a high barrier for his successor."