Wigan Athletic chairman Dave Whelan is hopeful Liverpool opt for Swansea City's Brendan Rodgers as their new manager.
• Swansea dismiss Rodgers talk
• Martinez wants Liverpool assurances
Liverpool are on the hunt for a new boss after they sacked Kenny Dalglish, who paid the price for poor home form in the Premier League.
A number of coaches have been linked with the post, with Wigan's Roberto Martinez set for a second set of talks with the Reds owners on Tuesday.
Swansea manager Rodgers has also been mooted as a candidate for the position, although the Welsh club stressed on Monday that the Northern Irishman will remain at the Liberty Stadium.
Whelan, though, has told ESPN: "If it is true that Liverpool want to speak with Brendan Rodgers it proves they don't know who they want as manager. I hope they choose Brendan Rodgers."
The Wigan chief also confirmed he wants a resolution over Martinez's future by the end of the week, adding: "Roberto has told me he is speaking with Liverpool again on Tuesday.
"I have now made it clear that I want this sorted out by Thursday at the latest as we have to get on preparing for next season."