It had been reported that Napoli, now managed by Skrtel's former Reds boss Rafael Benitez, had a recent £10million offer for the Slovakia international turned down.
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, who formed the central pairing with vice-captain Daniel Agger in the opening 1-0 defeat of Stoke.
But with fringe player Sebastian Coates suffering a serious knee injury playing for Uruguay , Rodgers says he may even need to strengthen at centre-half meaning a move for Skrtel would be extremely unlikely.
Rodgers was philosophical over the perceived snub of Tottenham-bound Willian to a switch to Anfield.
He added: "We think over the course of the summer we've been very ambitious. The attempt was to get in players to improve the team, some might say too ambitious but this is Liverpool Football Club, we're trying to get the best players we possibly can.
"As I said, it's one where if I can't get them it, we've just got to move on. We've got 11 days to go, we have to do anything we possibly can because it hasn't changed. If you're going to claim the league, you've got to have quality and you have to get the best players into your club to help you climb.
"That's our aim. So of course if you don't get the player you want, there's always that disappointment, you can't dwell on it.
"There's still a chunk of the window left and we did some business earlier on in the window, which was very good, and now if we can finish off in these remaining days and get some players in, it would help us and end a very good window for us."