Rodgers is regarded as one of the best young managers in the Premier League and was high on Liverpool's list of potential candidates to replace Kenny Dalglish, who was sacked on Wednesday following a disappointing league campaign.
Fenway Sports Group, the Merseyside club's owners, have had an approach to speak to Wigan manager Roberto Martinez accepted and were also keen to interview Rodgers, but it was widely reported on Friday that the 39-year-old Northern Irishman has turned down the opportunity to speak to the Reds.
The Guardian reported that Rodgers believes Liverpool should already know enough about his qualities to offer him the job if they feel he is the right man, rather than involve him in a drawn-out interview process that may feature several managers.
He is also said to be keen not to be seen to chase other jobs out of respect to Swansea.
Rodgers, who signed a new three-and-half-year deal in February, has previously been linked with Chelsea and Tottenham after making a huge impression by guiding Swansea to an 11th-place finish in their debut Premier League campaign.
Swansea were applauded off the pitch by Liverpool supporters after their impressive passing caught the eye in a 0-0 draw at Anfield earlier this season.
The Welsh club also rounded off their season by beating Liverpool 1-0 at the Liberty Stadium, a fixture which proved to be Dalglish's last in charge.
Former Barcelona coach Pep Guardiola, ex-England chief Fabio Capello, Norwich's Paul Lambert and Andre Villas-Boas, dismissed by Chelsea earlier this year, are also said to be on Liverpool's list of potential bosses.
Source: AFP
Source: AFP