The Sun says Atletico first tried to sign Suarez in January but met a dead end.
However a club insider said last night: “We know this is not an easy operation but we do not think it’s impossible.”
Atletico are convinced they are better placed to offer Suarez Champions League football.
But Suarez has said: “I’m at a club where I’m very happy, my family is happy. I’ve got great team-mates and a manager from whom I’m learning so much.”