It has been reported that Napoli, now managed by Skrtel's former Reds boss Rafael Benitez, have had a £10million offer for the Slovakia international turned down by the Anfield club.
Rodgers says that was news to him and he would have been informed had a bid been made.
When asked if there had been an approach, Rodgers said: "No, not at all.
"I haven't been told anything about that whatsoever. It was mentioned this morning but it is the first I have heard of it.
"Ian Ayre, our managing director, does a terrific job and he always informs me straight away of anything. I haven't heard anything."
Skrtel, 28, appeared to fall out of favour last season and faces increased competition for his place this term following the summer signing of Kolo Toure.
But with fringe player Sebastian Coates suffering a serious knee injury playing for Uruguay last week, Rodgers says he may even need to strengthen in central defence.
Rodgers said: "I think it is something we are looking at certainly, a player to come in in that position.
"One to strengthen the squad and two to allow some of our younger players to develop.
"I think to maximise Andre Wisdom's talent we need to get him some games and the idea is to get him out on loan.
"We can only do that if I get in someone with more experience to support the group."
Wisdom, 20, showed potential when operating at right-back last season but with Glen Johnson first choice in that position he did play in central defence in pre-season.
Coates, 22, has failed to establish himself since his arrival two years ago and had been linked with a move away before his injury.
Rodgers said: "I feel for big Seba. He has obviously played in the latter part of that game and picked up a similar injury to what Martin Skrtel had last year.
"It is probably going to rule him out for most of the season, which is a big problem.
"He's never given me a moment's problem since I came in here.
"This was probably a year where he needed to go out and play. This has unfortunately put an end to that."
One move Liverpool have made in the transfer market this week is to sign Valencia's French left-back Aly Cissokho on a season-long loan.
The 25-year-old, who has one France cap and has previously played for Lyon and Porto, brings strength to a position in which Rodgers only had Jose Enrique to call upon.
Rodgers said: "I think he provides competition for Enrique. He is a player with experience.
"A few years back he went for 15million euros. He is a player with qualities.
"The idea was to build a squad and to make it competitive. It was important to bring in someone so that if anything happens to Jose he can come straight into the team, and to fight for the position.
"Hopefully that will get the best out of both of them."