Dudek hoping to play on in Spain
The 38-year-old stopper - a hero of the Anfield club's Champions League final penalty shoot-out victory of 2005 - recently left Real Madrid having arrived in the Spanish capital in 2007.
During that four-year period at the Bernabeu he has largely acted as understudy to Madrid and Spain No.1 Iker Casillas, making just a dozen appearances.
Yet the former Poland international is keen to continue playing, telling Marca; "I have not thought about hanging up my boots yet. My family is very happy in Spain and in Madrid. My son has a girlfriend, so my priority is to stay in football without changing country.
"I have offers from Spain, Turkey and England. What is clear is that wherever I go, I will go there to play. Although I have been happy at Real Madrid and I consider it my home, it is now time to play again."
The Pole has been linked with a move to MLS side Seattle Sounders in recent weeks, with their current keeper Kasey Keller poised to retire at the end of the current season.