Wigan are set to hold a press conference on Tuesday where Roberto Martinez will announce his future plans.
Martinez has been heavily linked with the vacancy at Liverpool and is expected to reveal next week whether he will stay with the Latics or leave.
It is understood the 38-year-old met the Reds' owners in Miami this week to discuss the managerial vacancy and was not put off by the huge rebuilding job at Anfield.
However, it is understood Martinez has not made his mind up completely whether to accept that challenge and has given himself until Tuesday to do so.
Wigan chairman Dave Whelan claimed on Friday the Spaniard had received an offer from Liverpool's principal owner John Henry after their meeting in Miami on Thursday.
Martinez's appointment would doubtless divide opinion among Liverpool supporters, some of whom may have been expecting a bigger name to be recruited to replace the sacked Kenny Dalglish.
Throughout the process, Whelan has insisted it was not a foregone conclusion he would lose his manager to the club's north west rivals, claiming there were still some issues - mainly surrounding working under a technical director - to be overcome before Martinez would even be in a position to accept.
"He went to Miami and had a very constructive meeting with the owner of Liverpool," the Latics chairman told Sky Sports News.
"They're going to talk again on Tuesday. They've made Roberto an offer and he has agreed to consider it.
"He's said, 'What are my responsibilities?' These are American owners and the rules and regulations are a bit different from what we English set down.
"Roberto is a seven-days-a-week, 12-hours-a-day worker and I don't know whether they realise how hard he works.
"He has rules and regulations to be fully in charge of football and I know he won't move anywhere unless he is fully in charge of the football.
"I think he'll give it fair consideration. Hopefully, he stays with us but, wherever he goes, he's 100% dedicated to that football club."
