Wigan manager Roberto Martinez will hold talks with his chairman Dave Whelan on Wednesday afternoon as he seeks to clarify his future.
The Spaniard was widely regarded to be the front-runner to succeed Kenny Dalglish at Liverpool.
But the Anfield club have now renewed their interest in speaking with Swansea City manager Brendan Rodgers.
Aston Villa are also keen on Martinez, with Wigan privately fearful they will lose their manager in the coming week.
Martinez remains under consideration by Liverpool having held talks with owner John W Henry in Miami last week.
But, while Whelan had claimed his manager would hold a second round of talks with Liverpool's owners on his return from a holiday in Barbados, it is understood no such meeting took place on Tuesday.
Fenway Sports Group (FSG) hold both Martinez and Rodgers in the highest regard. Swansea rejected Liverpool's initial request for permission to open talks with Rodgers last week, but Liverpool have not been deterred and are keen to start negotiations.
Whelan has set Liverpool a deadline of Thursday to decide whether they wish to appoint Martinez.
Martinez also figures prominently in Villa's thinking - who are looking for a manager after sacking Alex McLeish - alongside Norwich manager Paul Lambert.
The Spaniard has been on Villa's radar for 12 months, having chosen not to take up an offer last summer to remain at Wigan.
Villa owner Randy Lerner and chief executive Paul Faulkner are keen to appoint an energetic, youthful manager. "We want to find someone to reinvigorate the club," Faulkner told BBC Sport earlier this month.
"We want someone to bring some vibrancy back to Villa. That's what we need and that's what we're going to get. A disaster would have been getting relegated but this was too close for comfort."
Intermediaries for Villa spoke with Martinez at the end of last week, while contact has also been made with representatives of Lambert.
Villa endured a disappointing campaign that saw them finish 16th in the Premier League, just two points above the relegation zone.