The La Liga side are confident they will be able to land the Liverpool forward if they secure qualification for next year's Champions League. Diego Simeone's team currently lie 2nd in La Liga, five points ahead of city rivals Real Madrid.
The report claims Atletico first tried to sign the Uruguayan international in January, but Liverpool rebuffed their attempts.
That hasn't deterred the Spanish side though, and they are ready to launch a stunning summer bid to lure the former-Ajax forward to the Vicente Calderon.
An Atletico Madrid club source told The Sun: "We know this is not an easy operation but we do not think it's impossible."
Suarez, however, is adamant he will still at Liverpool, and the Uruguayan star recently revealed how happy he is with life on Merseyside.
Suarez said: "I'm at a club where I'm very happy, my family is happy. I've got great teammates and a manager from whom I'm learning so much."
Suarez has started the Premier League campaign in sparkling form, and currently leads the Golden Boot race with 10 league goals.
But Liverpool currently sit 11th in the table, with 15 points from 12 games. The Reds have an opportunity to improve their standing this weekend, when they take on Swansea at the Liberty Stadium on Sunday.