The Colombian has spent two years at the Vicente Calderon and has enjoyed every minute of his stay in the Spanish capital but refused to confirm his exit
The Colombia forward is set to complete a €60 million switch to Monaco this summer, having helped the capital club win the Europa League, the European Super Cup and the Copa del Rey in a two-year spell.
Falcao is expected in the Principality this week for a medical ahead of completing the deal.
"I'm very grateful for these two years at Atletico Madrid," the 27-year-old told W Radio.
"I never expected to win three titles in so short time, this has been like a dream. Yesterday I lived a very emotional moment I had never lived before with the fans and a club.
"I will never forget it and I don't know how to give them thanks."
However, Falcao refused to confirm that he would leave the club in the summer: "Right now, I can't talk about my future, there will be time later."
Atletico Madrid president Enrique Cerezo also denied a deal for Falcao has been completed: "Falcao is yet Atletico's player. He is going to play a match [against Zaragoza] and after we talk about his future."
Meanwhile, Colombia are set to play Argentina on June 8 as their bid to qualify for the World Cup continues and Falcao is confident his nation can prevail in the clash.
He said: "Colombia have a great team with the capability to play in any field, any time, against any rival but we need to be discreet and think about what can we do against Argentina."