The Croatia international is set to be sold by Barca in January after finding himself surplus to requirements this season.
Movistar+ says Atletico have told Barca they will offer €40m for Rakitic ahead of the winter market.
Just this week, Rakitic admitted he was ready to leave Barca: "How can I have fun? By playing football.
“And it's like I often say, how does my little daughter feel when you take a toy away from her? Sad.
“Well, I feel the same. [Barca] have taken my ball away from me and I'm sad about it.
“I understand and respect the decisions of the coach, club or whoever, but I think I've given a lot in these five years.
“What I want is to continue having fun, that's the most important thing for me. I can only have fun by playing.
“I'm 31 years old, not 38, and I feel like I'm in my prime."