De Grandhomme may have decided to try his Big Bash luck, given that his decade-long international career appeared to be tailing off.
Mills said meetings over the next week should find a solution.
"There is more and more cricket being played around the world and the T20 competitions want players who are available for the whole tournament," Mills told NZME.
"And players get to a certain age, are not in the New Zealand team regularly, and other options become attractive. And that can't always happen with perfect timing.
"He hasn't been in the team a little bit of late…all those thoughts go around in a player's head."
The 20 New Zealand contracted players are required to play for the Black Caps and domestic matches, unless they are granted a no-objection certificate.
Mills said: "It could be that both parties mutually agree to terminate the international agreement but I don't want to pre-empt any outcomes."