The 39-year-old along with a list of high-profile managers have been touted to replace Kenny Dalglish at the Merseysiders after the Scot was sacked earlier this month.
A statement on the club's official website said: "We would like to clarify the speculation in the press surrounding our manager Brendan Rodgers.
"We would like to confirm that there has been no contact from Liverpool and nothing has changed since our previous statement on the issue."
Rodgers impressed in his first season as a manager in the Premier League guiding Swansea to an 11th place finish after many pundits believed they would struggle to adapt from the Championship.
The Swans style of play was also heralded around the league as they opted for the passing approach, often dominating the game in terms of possesion.
These credentials made Rodgers one of the alleged top targets after Dalglish and Reds parted company. However, the Northern Irishman declined to talk to Liverpool when offered the chance as revealed by the Swans.
A statement said: "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.
"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 Barclays Premier League campaign."
Meanwhile, Swansea are close to sealing the signing of Gylfi Sigurdsson for a club record £6.8 million fee after the club agreed personal terms with the midfielder and Hoffenheim.