The Daily Star says Liverpool are closing in on the Atletico Madrid striker, having watched him at recent games against Real Betis, and last weekend's match against Espanyol when Atletico won 3-2 after coming from behind with 10 men.
Forlan - who is also on Barcelona's radar - says he will decide on his future in the summer.
He said: "At the moment my desire is to score goals, to fight for the Golden Boot and to help Atletico to get a position in the Champions League.
"I will think about my future in June. I want a meeting with the directors and then to evaluate the situation.
"Do I want to return to the Premier League? In the world of the football anything is possible and I believe I have a debt with England after my time at Manchester United."