"Donald Trump hasn't done a whole lot for women during this campaign," Reagan told Don Lemon on "CNN Tonight." "And he's not doing anything now to bring women on board."
Reagan, who has been a vocal critic of Trump took to Twitter on Monday to vent in a flurry of tweets slamming the Trump campaign.
"My father would not support this kind of campaign, if this is what the Republican Party wants leave us Reagans out. Nancy would vote for HRC," he tweeted.
Lemon asked Reagan if he would tell Republicans to vote for Clinton.
"No, I would tell Republicans to vote their conscience," Reagan said. "I'm trying to protect the Reagan legacy."
Reagan cited Trump's latest attack on his Democratic opponent -- questioning, with no evidence, whether she is "loyal" to her husband as an example of what his parents would not support.
"This family's name is being dropped all over the place, every single day and inferring that Ronald Reagan would support these things and I have to say no, they wouldn't."
On the campaign trail, Trump has compared himself to the standard bearer for the Republican party. But Reagan said that he has written about his father's campaigns, referring to his book, "Lessons My Father Taught Me."
President Reagan told him that the main issue of a campaign is whether "you are qualified to be president of the United States, not if you're qualified to be a good husband or a good wife."
He told Lemon that he would love for the Republican nominee to reach out to him for insight, but "everybody instead wants to just have my name."
"He's trying to sell a bill of goods to get into the White House as the president of the United States of America." He added, "If that's the direction the Republican Party is going, fine, but leave the Reagans out of it."
CORRECTION: An earlier version of this article misstated Michael Reagan's mother.