The former pop star dated the 26-year-old singer-and-actress for 18 months when they were teenagers, but he now wants the chance to rekindle their romance.
Speaking to 'Entertainment Tonight', he said: ''I don't know who she is today, she doesn't know who I am today, but I would sweep her off her feet if I ever got a chance to again and fix what I did wrong.''
The former couple, who dated for three years, ended their on-again/off-again relationship in 2003 after Aaron cheated on the blonde beauty with Lindsay Lohan.
Aaron has previously spoken of his regret at cheating on Hilary with her then-best friend.
He has said in the past: ''I started dating Hilary on my 13th birthday... I was dating her for like a year-and-a-half and then I just got a little bored so I went and I started getting to know Lindsay, dating Lindsay.
''Then I didn't want to do that anymore, so I got back with Hilary. And then I ended up cheating on Hilary with her best friend. That's nothing to smile about. She wasn't even that good looking either.''
Earlier this year, Aaron declared his love for Hilary - who announced she had separated from husband Mike Comrie after three years of marriage in January - in a number of cryptic posts on Twitter.
He said: ''Don't be that stupid douche that loses the love of your life forever.. Like me..
''I'll spend the rest of my life trying to better myself to get back to her. (sic).''
His new album Underneath It All is out now.