The Latics boss was given permission to speak to the Anfield club after the departure of Kop legend Kenny Dalglish, but is just one of many potential candidates.
The Spaniard is also being linked with the vacant Aston Villa job after guiding the Latics to safety with wins over Manchester United, Liverpool and Arsenal in the second half of the season.
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With speculation mounting, Whelan admits the Lancashire club is in limbo and that a decision about the managerial situation will have to made soon.
He told the Wigan Evening Post: "Roberto will be in Barbados until next Tuesday, and I will then set a seven-day deadline by which time I will expect a decision.
"Until he gets back it's all quiet on the western front.
"I appreciate everyone is in limbo at the moment and there will come a time soon when we'll need an answer one way or the other.
"It is dragging on a bit but I only care about one thing - that is the future of Wigan Athletic. Nothing else matters.
"It's important we sort this out properly, one way or the other, so we can move forward in preparation for the new season."
Despite growing interest in his manager, the 75-year-old remains confident that he can hold onto his prized asset for next season.
He added: "I must stress to our supporters that I am by no means resigned to losing Roberto to Liverpool or any other club.
"He may go, he may not go. That will be up to Roberto and I will respect his decision either way.
"But it is not a foregone conclusion. Not at all. Hand on heart, I still believe Roberto will be here next season."