Previous manager Caldwell won promotion to the Championship last season after winning the League One title, but a poor start to life back in England's second tier cost him his job.
The Latics sit in 23rd position in the Championship with 11 points from 14 games and are currently three points from safety.
It is now being rumoured that Wigan want Ryan Giggs to replace Caldwell, in what would be the Welshman's first full-time job in management. Giggs previously had a spell in caretaker charge of Manchester United following the sacking of David Moyes and served as Louis Van Gaal's assistant for his two seasons at Old Trafford.
The 'Daily Mail' is reporting that the United legend would be open to the offer, but would demand a sizeable transfer budget in order to help the club avoid relegation back to League One.
Giggs was recently interviewed for the manager's job at Swansea, but the Swans opted for American Bob Bradley.