Wigan chairman Dave Whelan has given Liverpool until Thursday to complete a deal to bring Roberto Martinez to Anfield.
The 75-year-old has admitted that he will back Martinez's decision if he chooses to leave the club, but has become impatient, following reports that Liverpool have also approached Swansea's Brendan Rodgers about the vacancy.
"Roberto has told me he is speaking with Liverpool again on Tuesday," he told ESPN.
"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."
Martinez joined Wigan from Swansea in 2009, and his former club have insisted this week that there has been no contact from Liverpool regarding their current manager Brendan Rodgers.
And Whelan is hoping that the Northern Irishman will become the Reds first-choice for the post.
"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." he said.
The 39-year-old led the Welsh club to an impressive 11th place finish in their debut season in the Premier League, just five points behind Liverpool in eighth.
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