Records released in 2012 by Alaska officials revealed the former governor and vice presidential candidate once quipped about the possibility in an email.
The couple has been married for 31 years.
Track Palin, 29, allegedly assaulted a woman at his home in Alaska on Friday.
The former vice presidential nominee curtailed a Florida campaign trip for Donald Trump to return to Alaska.
The family of former Alaska governor and 2008 GOP vice presidential nominee Sarah Palin made headlines in September after allegedly getting into a messy brawl near Anchorage, Alaska.