Press Association Sport understands that the 39-year-old has rejected an approach from the Reds, who sacked Kenny Dalglish on Wednesday after finishing a disappointing eighth in the table.
Fenway Sports Group, the Merseyside club's owners, have already had an approach to speak to Wigan manager Roberto Martinez accepted and were also keen to interview Rodgers.
The Northern Irishman guided the Swans to 11th in their first season in the Premier League and is regarded as an exciting managerial prospect.
His teams are known to play slick, passing football, something which would appeal to Reds supporters. However he seems to have decided to continue his project in South Wales rather than attempt to jump into one of the most demanding jobs in English football.
Martinez kept Wigan up with a late surge in form, eventually finishing 15th in the 20-team table. He also prefers to keep the ball on the ground, having refused to change the Latics' approach during a difficult period of form in mid-season.
Liverpool have been linked with 11 potential managers in Friday's newspapers, with former Barcelona coach Pep Guardiola among their targets.