Liverpool have wasted little time in the search for Kenny Dalglish's successor by drawing up a wishlist headed by Pep Guardiola and Fabio Capello, and have already approached Roberto Martínez at Wigan Athletic, Swansea City's Brendan Rodgers and André Villas-Boas within 24 hours of bringing the Anfield legend's reign to an end.

Fenway Sports Group, the club's owners, received permission to hold talks with Martínez from the Wigan chairman, Dave Whelan, as their wide-ranging approach to identifying Liverpool's next manager became apparent a day after Dalglish's exit. Unlike Whelan, Swansea have not cleared the way for Rodgers to meet Liverpool as yet but are expected to do so. Villas‑Boas is also in the frame for the Liverpool job but John W Henry and Tom Werner, the principal owner and the chairman at Anfield respectively, intend to assess several candidates as they finalise a shortlist. Martínez, Rodgers and Villas‑Boas are by no means the only coaches under consideration. The ideal candidates are Guardiola and Capello but Liverpool's prospects of landing the outgoing Barcelona coach and former England manager are understood to be remote. Guardiola has previously stated his intention to take a sabbatical from the game following a trophy-laden but draining spell at the Camp Nou, while Capello is keen on the Chelsea job. Borussia Dortmund's Jürgen Klopp and Marseille's Didier Deschamp are also thought to be under consideration.

The Wigan chairman revealed: "When Liverpool sacked Kenny I have to say I thought Liverpool would be knocking on the door, and sure enough they are. I did promise Roberto when a big club comes he will have permission to talk to them and they don't come any bigger than Liverpool. I gave permission and he will be talking to them soon."

Martínez does not have the title-winning experience that forms part of FSG's criteria but he will get the opportunity to convince Liverpool's owners that he can fit into the new management structure they intend to install at Anfield. Whelan said: "We played there [at Liverpool] about two months ago. There's no heart at the club. It's a bit disturbing when you think a club like Liverpool is functioning without a heart. I mentioned that to Roberto and I think there's no heart beating at Liverpool. I think the sooner they get a heart the better. I don't know Roberto's feelings about Liverpool, I think he's going there with an open mind. I would love to keep Roberto, he's a great manager."

Liverpool's managing director, Ian Ayre, claimed the selection of Dalglish's successor represented the most critical in the club's recent history. He also insisted Anfield remains an attraction for the finest managers in the game. FSG are being advised on the process by "highly regarded people within football", according to Ayre, who revealed the next manager must work under a new management structure at Anfield. Damien Comolli's former role as director of football is to be fragmented this summer although the new manager will continue to have an influence on transfers.

Liverpool face a third season outside the Champions League next term and Uefa's financial fair play rules, which requires clubs throughout Europe to break even, come into effect in 2013‑14. The failure to mount a challenge to the top four this season, and FSG's doubts over Dalglish's ability to deliver one next year, cost him his job despite winning the Carling Cup and reaching the FA Cup final.

Asked if Liverpool had made a more important appointment than the one now confronting Henry and Werner, Ayre said: "No. It's absolutely critical that we get it right and we move forward. The Champions League is where the football club has to be. When John and Tom arrived, they said they wanted to win. They mean winning and being in that competition. They want to be winning the league. It won't happen overnight. Nobody is kidding themselves. But you have got to be heading in that direction."

Replacements for Comolli – with his old job to be divided between its administrative, scouting and negotiating functions – Graham Bartlett, the former commercial director, and the head of communications Ian Cotton are expected in the next fortnight. The managerial search, said Ayre, who recently had his contract extended at Liverpool, is based "on a whole range of things, from experience and ability, methodology, style of play, character traits. As we've seen in the past it is not just about the football. It is about how controlling some are compared to others. There's a particular process that fits part of the plan we are trying to put together. It has to be a manager who fits in all of that."

Ayre's "controlling" comment would appear to rule out Rafael Benítez from a Liverpool return, the former manager having been given control over all football operations in his final contract.

David Dein, the former vice-chairman of Arsenal, was spotted at several matches with Liverpool officials towards the end of the season but Ayre refused to confirm who is advising Henry and Werner. Villas-Boas, Klopp and Deschamps all meet the criteria of younger title-winning coaches but, having again failed to qualify for the Champions League, and appointed from Fulham (Roy Hodgson) and within (Dalglish) for its last two managers, Ayre denies Liverpool are struggling to entice the most coveted coaches.

Ayre added: "Liverpool still gets everyone excited and interested. We may have lost our way a little in terms of performances but it is still one of the biggest football clubs in the world. It still has a huge fan base. It has also got a good solid business foundation. It has got good owners who are committed. A lot of that doesn't exist in a lot of other football clubs. If you are a manager at that level or you are a manager aspiring to get there, I still think this is one of the biggest jobs in world football.

"I am under no illusion that we can go and find a top-class manager to come to this football club, for all the reasons I have stated. I do not think we are in a situation where the very experienced, very capable, very driven managers who people would want to see here do not want to come."