The Daily Star says Kop boss Rafael Benitez has struggled to find a left-winger for his under-pressure team. But now he is thinking of turning to the Atletico Madrid wide man.
Simao starred in Atletico's Europa League semi-final win over the Reds, and their victory over Fulham in the final.
But he is 30 and Atletico need some cash to start adding players to their side.
Simao has only a year left on his contract in Spain and would welcome a move to the Premier League.
He said: "Nobody has spoken with me in the last days about this subject.
"I only say that some people in Madrid have suggested that Atletico are preparing my sale, but I don't know too much.
''I have always been interested in playing in the Premier League, but my head is in the World Cup and I have a deal with Atletico."