If the aproach to sign button is no longer available then that would suggest to me that they have signed a new contract. If you want them then you will just have to put in a regular transfer bid for them.
Are the Asian players from more obscure nations by any chance?
I have also noticed this with unattatched players from nations such as Laos, yet with players from a more reputable nation such as China, this isn't a problem.
This never seems to affect players from other continents however.
Maybe the rules in Asia are different to Europe and signing youngsters is not allowed?
I tried to get a 16-year-old regen from Brazil (not on a free transfer) and he can only join when he turns 18, which seems to be a specific rule for Brazil.
There may be similar rules for the country (countries) from which you were looking to sign a player.