The Colombia international joined Premier League side Everton from Real Madrid in September after struggling for playing time under Zinedine Zidane last season.
He was linked with a number of high-profile suitors before completing his eye-catching switch to Goodison Park for what later transpired to be a free deal.
Atletico were among the sides tipped to sign James at the time and the 29-year-old has revealed he was close to joining Real's city rivals.
"It was nearly a done deal to got to Atletico," he told ESPN. "I spoke with Simeone, he said I could be important, but Real didn't let me go.
"[President] Florentino Perez knew that with Zidane there I wouldn't play much. It was a bad year and I wanted to come to Everton to play and show what I can do.
James has scored five goals and registered four assists in 18 Premier League appearances this season.
That puts him level with Richarlison for the second-most goal involvements of any Everton player in the league this term, behind only striker Dominic Calvert-Lewin (14 goals).
No Everton player has created more chances than his total of 31, meanwhile, with 23 of those from open play - another team high.
James has enjoyed a positive first campaign in English football, but he would not have considered joining Everton without the presence of three-time Champions League-winning coach Carlo Ancelotti.
"I'll say it with all sincerity that if Carlo wasn't here, I wouldn't have come," said James, who has not featured since February because of a thigh injury. "I'll say it with all my heart, he was one of the reasons for which I came.
"I have started to get to know the club, how they work, how they want to work, win things, play in Europe. The fact that Carlo is here was fundamental to come here, where I am learning every day.
"In these remaining [league] matches, I want to perform well. I had some physical problems for a month, but I have overcome them and it's my goal to get a European spot, hopefully in the Champions League."
Everton are eighth in the Premier League, five points behind fourth-placed Chelsea with a game in hand.