Roberto 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.

"Roberto has had a constructive meeting with Liverpool. He is now back at my home in Barbados," revealed Whelan, who will demand around £3m in compensation for Martínez to join Liverpool. "He returns to London on Tuesday, when he will have further talks with Liverpool and when a decision will be made.

"There was no other manager mentioned so I imagine they want Roberto. I don't want to lose him, but I made him a promise when he first joined that, if a big club came in for him, I'd let him go, and I will honour that promise."

Whoever takes the Liverpool manager's job will have to accept working alongside a sporting director-type figure as FSG overhaul the structure at Anfield following the dismissals of Dalglish and former director of football Damien Comolli. Louis van Gaal is the leading candidate and Whelan, who has claimed the new manager will not have responsibility for transfers at Liverpool, believes FSG's strategy could deter Martínez from moving to Anfield were he to receive an offer.

The Wigan chairman added: "I am still not convinced it is a foregone conclusion, because they put their points on the table, and Roberto put his. He listened to their points, but I think they also listened to his and I think they are coming to terms with the way English football is run. Roberto wants control over football matters and that includes transfers, and if they agree to that, then I can see him becoming the Liverpool manager.

"Roberto works seven days a week, sometimes 12 hours a day. He is not the average manager, but he likes to run the football side, and I can see Liverpool's point of view about the amount of money spent on players. If they agree to let Roberto take responsibility for the transfers than I think he will go there, and I can see that Liverpool have set their sights on him."