Wigan Athletic chairman Dave Whelan has warned Roberto Martinez against taking the Liverpool job, suggesting that the Reds "don't know what they are doing".
Whelan confirmed on Thursday that he has granted Martinez permission to speak with Liverpool, who are seeking a successor to sacked manager Kenny Dalglish.
The Reds' shortlist for a new boss is said to be extensive - as many as ten names in the frame - and among those targets was Swansea City coach Brendan Rodgers.
But Rodgers has rebuffed Liverpool's advances as he is settled at the Liberty Stadium, and Whelan feels the Ulsterman's actions should serve as a warning to Martinez.
He told ESPN: "When Liverpool asked for Wigan's permission to speak to Roberto, it was willingly given, and you would have thought they wanted him for the job. But now it transpires they are looking at quite a few possibilities.
"The fact that Brendan Rodgers has opted out after they approached Swansea should get Roberto thinking he might be better off at Wigan. There is a suspicion that Liverpool don't know what they are doing, certainly it is clear now they don't know who they want as manager."
Liverpool's managing director Ian Ayre, though, is confident that the club can still attract the profile of manager they are aiming for, despite the lack of Champions League football once more next season.
"We will find out (the effect of not being in the Champions League) during the process I guess. The reason I don't think it will have an effect is if you lined up most managers in football and asked them if Liverpool would be a great club to manage and most people would aspire to do so I think they would say yes," Ayre said.
"The history of this club, the reach of this club around the world , its fanbase and everything we have achieved and want to achieve is more than enough to keep any manager we would want to go after hungry for the opportunity.''