Liverpool are confident of appointing Jürgen Klopp as their next manager and could install the 48-year-old as Brendan Rodgers’ successor by the end of the week.

The club’s owner, Fenway Sports Group, moved swiftly to approach representatives of the former Borussia Dortmund coach after sacking Rodgers on Sunday. The initial talks have been encouraging for FSG, with indications Klopp will abandon a sabbatical to take the Anfield vacancy.

Negotiations, which are being led by Mike Gordon, FSG’s president, will continue over the coming days – with the German’s acceptance of working with Liverpool’s transfer committee yet to be addressed – but Anfield officials are increasingly confident of securing Klopp’s services and doing so quickly.

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It is understood Klopp’s former assistant at Dortmund, Zeljko Buvac, and the coach, Peter Krawietz, would join him at Liverpool should talks continue to proceed smoothly. Their arrival would raise doubts over the Anfield futures of Sean O’Driscoll and Gary McAllister, the assistant manager and first-team coach respectively, who only moved to Liverpool last summer as replacements for Colin Pascoe and Mike Marsh.

Liverpool have still to agree a compensation package with Rodgers, who issued a statement through the League Managers Association on Monday, expressing disappointment at FSG’s decision but also his thanks for the opportunity to manage the club. The Northern Irishman, who has gone to Spain on holiday following his dismissal, could be entitled to up to £10m for the three years that remained on a contract he signed in May 2014 but is expected to be offered £7m.

Klopp’s current availability is believed to have been a factor in FSG’s decision to sack Rodgers before the international break and go for a manager coveted throughout Europe. The charismatic coach is on an extended break from the game following a seven-year spell at Dortmund that saw him win two Bundesliga titles and appear in the 2013 Champions League final. He has been touted as a potential successor to Pep Guardiola at Bayern Munich should the former Barcelona coach leave next summer but the lure of a rebuilding job at Anfield and working in the Premier League also appeals.

FSG intends to persevere with the transfer committee that saw such poor results during Rodgers’ reign and Klopp’s role within it may yet prove a complication, although he delegated over player recruitment at the Westfalenstadion.

Liverpool’s refusal to appoint a caretaker manager in the wake of Rodgers’ dismissal is another indication of their confidence in a swift appointment.

O’Driscoll and McAllister have been left to work with players not on international duty this week, with FSG aiming to have its new man in place for the trip to Tottenham Hotspur on 17 October. A deal for Klopp could be concluded long before then.

FSG said it intended to appoint in a “decisive and timely manner” when announcing Rodgers’ departure. Though Carlo Ancelotti is also out of work and has been considered by FSG, and Frank de Boer of Ajax has expressed interest in taking over at Anfield, Klopp is Liverpool’s overwhelming first choice.

The former Germany midfielder Stefan Effenberg, a friend of Klopp, believes the former Dortmund coach would be a perfect fit for Liverpool. Effenberg said: “He gave me this answer a couple of weeks ago. He said: ‘I’m ready for a team that’s not on the highest level, to create something, to build something up.’ This could be Liverpool, right?”

Effenberg added: “Liverpool is one of the greatest atmospheres. It’s pretty much the same as Dortmund. The fans stay with everything behind the club and this is what Jürgen Klopp likes and what he needs. So maybe, very soon, we’ll hear something from Jürgen Klopp, to make a decision, maybe, for Liverpool.”

Rodgers reiterated his belief that Liverpool are a team in transition in his LMA statement, but was gracious in his leaving. “I am, of course, incredibly disappointed to be leaving Liverpool football club,” he wrote. “It has been both an honour and a privilege to manage one of the game’s great clubs for the last three years.

“I have worked every day to represent the club to the best of my ability, to develop both individual players and a team that the club’s magnificent fans can be proud of. There have been some very memorable moments during my time at Liverpool and I would like to thank all of the players for their hard work and commitment. The current squad is one in transition, but they have some real talent and are showing a strong sense of togetherness.

“I expect to see them continue to grow and develop over the coming weeks and I wish them and my successor well for the rest of the season.”

Having thanked supporters and all those connected with the club, he added: “Finally, I would like to give a special mention to John W Henry, Tom Werner and Mike Gordon. They gave me this great opportunity and even though we will no longer be working together I am sure our relationship and friendship will continue into the future.”