The Spanish midfielder is set to sign a five-year contract with Atletico subject to a medical.
The 24-year-old, who made just 16 appearances for Real last season, will move for a reported £35m.
The move of llorente could pave the way for Rodri to complete a move to Premier League champions Manchester City, who are ready to pay his release clause.
Rodri told Atletico earlier this month that he wanted to leave the club for a new challenge. He has also interested Bayern Munich.