The two South American forwards, who have both turned out for Manchester United, have been prolific goalscorers in Europe in recent years.
Atletico Madrid president Enrique Cerezo has been discussing transfer prospects on Spanish media outlet Radio4G, according to quotes from Sky, letting slip that the Spanish club are tracking two former Manchester United forwards.
“We are going to bring in two or three reinforcements," the 67-year-old said in Radio4g. "But the Falcao one and the Tevez one are very difficult.”
The two players have an unusual place in United's history, with Carlos Tevez impressing after arriving from West Ham, helping the club to the Champions League trophy in 2008. Whatever good he did at the club was undone by his switch to rivals Manchester City though, despite the Argentine moving on to Juventus, where he seems to have found his first settled European club.
Falcao is an even more peculiar player, arriving on loan at the start of this season just gone widely acknowledged as one of the world's best strikers, the Colombian found it impossible to seize any form at Old Trafford, and finished the season with just 4 goals in 29 games.
The Colombian, who has also been linked with Chelsea by the Mirror, is a familiar figure at the Vicente Calderon Stadium, where he scored an astonishing 70 goals in 91 games in a two-year spell between 2011 and 2013.
Either player would be a quality if expensive addition for Atletico, who are still looking for a forward to replace Diego Costa.