Liverpool are confident a deal with Jurgen Klopp will be reached by the end of this week.
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.
Liverpool have still to agree a compensation package with Brendan Rodgers.
The availability of Klopp contributed to Liverpool's decision to fire Rodgers.
Liverpool’s refusal to appoint a caretaker manager in the wake of Rodgers’ dismissal is another indication of their confidence in a swift appointment.