"Swansea City can confirm that an approach from Liverpool FC to speak to manager Brendan Rodgers was officially received by club chairman Huw Jenkins this morning," a statement said.
"The club is pleased to confirm that Brendan has declined the current opportunity to speak to the Anfield club about the vacant position.
"The Swansea manager is currently working hard to strengthen the squad in readiness for the new Premier League campaign."
Rodgers guided Swansea to promotion via the playoffs last season, becoming the first Welsh club to reach the Premier League having last played in the top flight in 1983.
Widely-tipped to struggle, Swansea won plaudits for their passing game and finished a respectable 11th, finishing their season off with a 1-0 victory over Liverpool that proved to be Dalglish's last game in charge.
Several names have been linked to the Anfield job, including former Swansea boss who helped Wigan Athletic avoid relegation for the second season in a row.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.