Reports have suggested Falcao, 27, who has a price tag of around 60 million euros ($77.6 million), is poised to join Monaco, who have just won promotion back to France's Ligue 1 and have an ambitious billionaire Russia owner.
Atletico coach Diego Simeone reminded reporters at a news conference that Atletico had not made any official comment on Falcao's possible exit but did little to dispel the sense of inevitability that the player was leaving.
"What more can I say, just thanks for what he has given us if he has to leave," Simeone said.
"Everything that happens to Falcao makes me happy," added the Argentine, who coached the Colombian when they were both at River Plate.
Monaco have already signed Joao Moutinho and James Rodriguez from Falcao's former club Porto for a combined fee of 70 million euros.
Monaco are at odds with French football authorities over tax exemptions but they have attracted many leading players helped by the fact that, under the principality's laws, foreigners do not pay tax on their wages.
The French League (LFP) has ruled that the club must move their head office to France by the beginning of June 2014, meaning players would pay tax in France.