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 midfielder] 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.
Celta survived relegation on the final day and since then the Reds have been trying to finalise arrangements for the 25-year-old to visit the club's Melwood training ground for physical assessment.
That is expected to be advanced in the new couple of days with the playing telling Spanish media over the weekend: "I was forced to cancel my holiday in the Caribbean but the reason I did more than justifies why.
"When I heard of Liverpool's interest I did not hesitate even for a minute.
"Liverpool is one of the biggest clubs in the world and although I had offers from Italy and Portugal and other countries I decided my future was in English football."
Aspas is set to Rodgers' second signing of the summer, following Kolo Toure to Anfield after the centre-back's contract expired with Manchester City.
A third could also be in the offing in the form of Luis Alberto but further movement cannot be made on that until later this week at the earliest.
The 20-year-old has been on loan at Barcelona B from Sevilla and the Catalan club have first option to sign the striker permanently but Press Association Sport understands Thursday appears to be decision day on that front.
Alberto, who scored 11 goals in 37 second-tier appearances, has been capped by Spain Under-21s.
"It would be foolish and deluded for me to say no to a club like Liverpool but as far as I know, there's nothing," the youngster told Spanish reporters at the weekend.
Rodgers is keen to offload striker Andy Carroll, who is stalling on a move to West Ham where he spent last season on loan despite a deal worth £15million-plus being in place for several weeks.
The delay does not appear to have put off the Hammers, with boss Sam Allardyce telling whufc.com: "At this moment in time, our first priority is signing Andy Carroll, if we can.
"(The off-season is) about the recruitment of the other players who we want as quickly as we possibly can.
"That will be the most difficult part of this summer."