Palace have been linked with a move for the Australian for some time and Ian Holloway has now reportedly stepped up his efforts to complete a deal before Monday night's deadline.
A bid in the region of £600,000 is understood to have been made and the 28-year-old's representative says he would jump at the chance to play in England.
"A sizeable offer has been made and the player hopes to fulfil a lifelong dream," Milligan's agent Buddy Farah said in the Herald Sun.
Farah is also acting as the Australian agent of former Tottenham Hotspur defender William Gallas, who has been linked with both Crystal Palace and Melbourne Victory.
However, Palace manager Ian Holloway admitted over the weekend that a deal to bring in Gallas was unlikely to be sealed.
"Whether we can ever come to a deal I do not know. He was a very nice man and he admitted he is only 50 per cent fit, which might be a problem," Holloway said.