Kakuzu. He's all about money and assets. If he thought that rescuing the female OC could lead to some sort of financial gain, he'd be the one to start the rescue. Maybe she has information about a rich bounty or a hidden cache of valuable ninja tools.
Deidara. He might be attracted to the female OC's unique appearance or abilities. He loves things that are 'artistic' in his eyes. If he saw the OC as some sort of living art or a potential source of inspiration, he could be the one to initiate the rescue, regardless of what the other Akatsuki members think.
Itachi. He's one of the more complex and morally gray members of the Akatsuki. If he saw that the female OC was in a situation that could potentially cause chaos or harm to the ninja world in a larger sense, he might initiate the rescue. He's also the type who might see some value in the OC that others don't.