Speculation about the Slovakia international has been widespread ever since he lost his first-team place to the now-retired Jamie Carragher in January. He has recently been linked to a reunion with Rafael Benitez - the man who took him to Anfield - after the Spaniard was appointed Napoli coach.
And although agent Karol Csonto has told the Italian club they will have to approach the Reds first, he did not dismiss the idea of the 28-year-old moving to Serie A. "There has been no contact between the two clubs. Martin has a contract with Liverpool and it is important to honour that," he told Italian station Radio Crc.
"Obviously Napoli know Martin well, but there cannot be any contact between us and them if they do not first reach an agreement with Liverpool. Between Martin Skrtel and Rafa Benitez is a professional relationship that has gone on from the years they spent together at Liverpool. [Napoli's] Marek Hamsik and Skrtel are very good friends and they met last week.
"The midfielder requested information from Martin about Benitez, while Skrtel has asked questions about Napoli. But I think that if Napoli want to take Skrtel, they should first talk to Liverpool. I will be in England next week to talk with Liverpool and define Martin's future."
Liverpool are tracking Schalke centre-back Kyriakos Papadopoulos as a replacement for Carragher but they also have interest in other targets as the future of Skrtel and Sebastian Coates means there could be a major reshuffle in defence.
Ajax's Toby Alderweireld is also believed to be on Rodgers' watch list and the player gave the Reds boss every encouragement by stating his intent to move to England.
"England and Germany are the best leagues where I think I can take the next step," the 24-year-old Belgian told De Telegraaf.
"I have to go somewhere where I can play football a bit and where my style of play suits. On the other hand, I do not want to play for a team at the bottom of their league. I want to leave Ajax for a nice club, otherwise I'll just stay in Amsterdam."
One player closer to an Anfield switch is Celta Vigo forward Iago Aspas, who is due on Merseyside for a medical. A deal worth about £7.7million has been in place for a couple of weeks but progress was held up by the end to the Spanish season.