Wigan Athletic boss Roberto Martinez is set for a new round of talks next week.
The Guardian says Martínez will hold further talks with Liverpool's owners on Tuesday as he considers whether he can work within the new management structure that Fenway Sports Group wants at Anfield.
The Wigan Athletic manager met John W Henry, Liverpool's principal owner, in Miami on Thursday for what his chairman, Dave Whelan, has described as "constructive talks". Whelan also claimed the 38-year-old was offered the job of succeeding Kenny Dalglish as manager but Liverpool deny that any offers were made.
Henry and Tom Werner, the Liverpool chairman, will travel to England early next week to interview several candidates for the post and still wish to speak to the Swansea City manager, Brendan Rodgers.