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 pending exit.
The Colombia forward is reportedly set to complete a 60 million euro 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. He played his last home game of the season at Estadio Vicente Calderon Sunday, going the distance in a 0-0 draw with Mallorca and has one more game remaining this season, on the road at Real Zaragoza.
"I'm very grateful for these two years at Atletico Madrid," the 27-year-old Falcao 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."
Falcao, whose 28 league goals trail just Lionel Messi's 46 and Cristiano Ronaldo's 34, refused to confirm that he would leave the club in the summer, saying: "Right now, I can't talk about my future, there will be time later."
Colombia is set to play against Messi' Argentina on June 8 as its bid to qualify for the World Cup continues, and the forward is confident his nation can prevail in the clash.
"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," Falcao said.