Bank of America's CEO says a pre-crisis idea could make it easier for millennials to buy homes

Mortgage lending standards have tightened since the housing bubble brought down the financial system a decade ago.

While homeownership has fallen, home prices have jumped back to precrisis levels, suggesting that the cost and requirements for getting a mortgage are holding back many would-be buyers.

Brian Moynihan, Bank of America's CEO, told CNBC that eased regulations including a lower down payment could make it easier for millennials, in their household formation years, to buy homes.

"Our goal, going back to regulatory reform, is should you move the down payment requirement from 20% to 10%? Wouldn't introduce that much risk but would actually help a lot of mortgages get done," Moynihan told CNBC's Kelly Evans.

Evans had asked Moynihan about mortgages in the context of widely shared comments from Australian tycoon Tim Gurner last week, which suggested millennials should stop spending on avocado toast if they want to afford homes.

Moynihan said he shared the article with his son and added:

"I think at the end of the day people forget that, at different points in your life and different points on what you're doing in life requires you to think about housing differently as a place for you and your friends, as a place for you and maybe your significant other, and then ultimately, a place for family. That drives change. And so yes, it's taken more time. And we talked a lot about this, you know, four or five years ago, that if you require a 20% down payment, it takes just a little more time to accumulate 20% than it would 3% or none, which is what the rules were for a short period of time."

Leading up to the recession, some lenders lowered the 20% down payment standard or required no down payment at all.

The scars from the housing crisis now make lenders cautious of who they approve. In the first quarter, the median credit score of a new mortgage was 764, the highest in nearly two years and up from the prerecession average of 720, according to Gluskin Sheff.

And according to Moynihan, there's still wiggle room to ease regulations.