The 28-year-old, also linked with Queens Park Rangers, is valued at close to £1million by his club.
But Melbourne say that Palace's bid falls short of their valuation of Milligan, who can play in midfield and defence.
"We haven't had a bid of $1.5million from Palace. We have had a bid from Palace, but it's fallen short of our valuation," coach Ange Postecoglou is quoted by The Age.
"'I understand that Millsy is a highly sought after player. He enjoys this club, and he understands he is in this position because of this football club.
"So there is a whole range of things (to consider). We have a responsibility to our own supporters, we are going to have 28,000 members this year and 50,000 at our first game.
"I take that responsibility very seriously. He is the best player at our club, I think he is the best player in the country at the moment, so I don't think we need to be out there trying to flog him and we are certainly not doing it for the money.
"We are looking for him to lead in that area (midfield). As I stand here right now I am (confident in him being a key part of the team). He's contracted for another two years and he's a very important part of what we are building here.
"We value him very very highly, and if somebody was to look to prise him away from us we would expect them to meet our valuation of him."