Liverpool will hold talks with André Villas-Boas next week over the managerial vacancy at Anfield but their wide-ranging approach to finding Kenny Dalglish's successor has resulted in Brendan Rodgers rejecting an interview offer from Fenway Sports Group, the club's owners.

Villas-Boas, who guided Porto to the Portuguese title and Europa League before an ill-fated spell at Chelsea, discussed a possible move to Roma this summer but, with the Italians going for Vincenzo Montella, has made it known he would be interested in a second stint in English football with Liverpool. Anfield officials have scheduled talks with the 34-year-old and the Wigan Athletic manager Roberto Martínez for the coming days as they accelerate the process of replacing Dalglish.

Pep Guardiola and Fabio Capello top the wish-list but Liverpool have not received encouragement from that pair. Jürgen Klopp, the double-winning coach of Borussia Dortmund, cannot be tempted from Germany. Rafael Benítez, who has made no secret of his desire to return to the club where he won the Champions League in 2005 and still lives on Merseyside, has not yet been approached although John W Henry, the principal owner, may consider an approach to the Spaniard depending on the outcome of talks with other candidates next week.

FSG are putting together a new management structure at Liverpool and doubts have been voiced over Benítez's willingness to work as part of that team given the control he sought, and received, during negotiations for his final contract at Anfield. However, the 52-year-old worked under a technical director both before he joined Liverpool, at Valencia, and afterwards, at Internazionale.

Liverpool's exhaustive interview process invited ridicule on Friday when a post on the club's official Twitter account asked: "Who do you want to replace Kenny Dalglish as #LFC manager? Reply with your suggestions and reasons." The club later said the tweet was "misunderstood – we were simply looking for fan views to include on a fun online feature". It also deterred Rodgers from accepting Liverpool's approach.

The Swansea City manager was invited for an interview but declined on the basis that Liverpool should be fully aware of what he brings to the table. Rodgers is also conscious of how disrespectful it would look to the Swansea supporters if he was seen to be chasing, rather than being offered, another position.

The 39-year-old signed an improved three-and-a-half year contract at Liberty Stadium in February and although he is hugely ambitious, there is no sense that he needs to go looking for opportunities elsewhere, especially at a time when he is trying to build a team at Swansea. Talks are ongoing in relation to signing Gylfi Sigurdsson, who was such a revelation on loan last season. There is also a feeling among those close to Rodgers that Swansea's performance at Anfield in November, when they were applauded off the pitch by the Liverpool supporters, together with the 1-0 victory over Dalglish's team on the last day of the season, should provide more than enough evidence of his qualities, as opposed to being part of a formal interview process.

Rodgers, who is also on the shortlist for the managerial vacancy at Aston Villa, has seen his reputation grow on the back of Swansea's outstanding first season in the Premier League, when they finished 11th and were widely acclaimed for their easy-on-the-eye playing style.

A Swansea statement said: "Swansea City can confirm that an approach from Liverpool FC to speak to manager Brendan Rodgers was officially received by 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. The club will make no further comment at this stage."

Liverpool, meanwhile, are to appoint Jen Chang, the senior editor for football at sportsillustrated.com, as their new head of communications.