Louis van Gaal says Manchester United have offered David de Gea "a lot of money" in a bid to keep him at Old Trafford.
But 26-year-old Falcao thinks he will stay at Atletico until at least the end of the season.
He said: "I recognise the great effort made by (Atletico president) Enrique Cerezo for me to stay at the club.
"I thank God our results have been so positive and that we have done so well this season so far. My expectation is that I will be staying at the club until the end of the season."
Atletico will welcome the words after sporting director Jose Luiz Perez Caminero gave an insight of the hard work made to keep Falcao at the club.
Caminero said: "You have to appreciate the efforts made by the club. It is difficult to keep a player of his class.
"But we have all benefited and are happy to have one of the best players in the world at this club."