Liverpool's owners reportedly met with Michael Edwards in Boston on Sunday to discuss a potential return to Anfield.
Edwards, who played a key role in the club's transformation under Jurgen Klopp, stepped down as their sporting director after a 10-year association with the Reds back in 2022.
It was revealed in January that he had rejected the chance to return to Anfield and lead a widespread restructure, following Klopp's shock announcement that he will leave the club this summer.
The Times have now reported that he has held face-to-face talks with the club's owners as they continue to persuade him to return to the club.