The former Reds sporting director is in advanced talks about taking the football chief executive post at Liverpool, replacing Billy Hogan, who is set to take full charge of FSG and their portfolio.
The Sun says Edwards will be in charge of all football decisions at Liverpool, with former Bournemouth chief Richard Hughes to also be appointed as technical director.
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Edwards will be given full responsibility to find manager Jurgen Klopp's replacement as he steps down this summer.
He was flown to Boston last week for talks with FSG powerbrokers about the role.