The 29-year-old Portuguese international has made 63 league appearances for the rojiblancos since arriving from Benfica in 2007, after netting 97 league goals from midfield for the Lisbon giants.
Reds' boss Rafael Benitez has been linked with a move for diminutive playmaker in the past, with the midfielder netting a stunning goal at Anfield for Benfica in 2006 to knock out the then European champions.
And, according to Diario de Noticias, the Merseysiders submitted a £19 million bid for Simao shortly before the summer transfer window slammed shut.
However, Abel Resino's side rebuffed Liverpool's advances for the player - who has won 71 caps for his country - with Atletico desperate to keep hold of their prize assets, including Sergio Aguero and Diego Forlan.
Serie A side Juventus were also reportedly interested in securing Simao's services.
