The Duke cannot agree terms with the club and is set to see his contract out unless a better deal is offered.
The Latics are now expected to sell the striker who helped them seal promotion to the Premiership last season.
"We met with Wigan last week and their offer was turned down," Finnigan (Ellington's agent) told skysports.com.
"Nathan has decided to see out his contract at the club. Should they wish to sell him before his deal expires, then that is up to them."