The 27-year-old is one of the most coveted players in world football, with many predicting he will move this summer.
Contracted to Atletico until 2016, he has a release clause of just over £50million.
The player himself has kept his counsel and always insisted he was concentrating on getting Atletico into the Champions League - a feat they are about to achieve this term.
Real Madrid, Chelsea and Manchester City were widely considered to be heading the chase for the Colombian star but now it has been claimed that Manchester United have made a move.
Atletico sources have told Sky Sports that they are not looking to make any comment on the speculation as they are not thinking about the transfer market at the moment.
"The rumours are habitual about our player, but now Atletico is only focussed on the sporting question and not about the subject of the transfer market," a source said.
Atletico Madrid coach Diego Simeone took the speculation in his stride though, telling reporters on Wednesday afternoon: "The same thing happened at the same stage of the season last year. It's not news.
"Falcao is a great player and it's logical that the best teams in the world are interested in him. It doesn't surprise me."
Atletico paid a club-record 40million euros to sign Falcao from Porto in 2011 and in his first season in Spain he scored 36 goals in all competitions.
The 27-year-old has continued that form this campaign, notching 28 times already to help the Rojiblancos reach the Copa del Rey final and mount a bid for a top-two finish in La Liga.
Atletico are currently third in the league standings, three points behind second-placed Real Madrid, with eight games to go. They also play Real in the cup final next month.