The trouble is there is just not that much out there to buy. Home construction is still recovering at a slow pace, and prices for newly built homes are far higher on average than for existing homes.The number of homes for sale is rising slightly but is still well below historical norms across most markets.
"Even after a wrenching housing recession, this data shows that the dream of homeownership remains very much alive and well, even in those areas that were hardest hit," Zillow's chief economist Stan Humphries said in the report. "But these aspirations must also contend with the current reality, and in many areas, conditions remain difficult for buyers. The market is moving toward more balance between buyers and sellers, but it is a slow and uneven process."
Homeownership aspirations among renters were actually highest in some of the hardest hit markets of the housing crash, such as Miami, Atlanta and Las Vegas, according to Zillow. That may be because so many renters there are former homeowners who lost their homes to foreclosure. They are now seeing these markets recover, as investors bought up the distressed properties, pushing prices higher far faster than anyone expected. These renters are seeing market resilience, and likely want back in.
(Read more: What happens to prices when Wall Street is your landlord)
Foreclosure activity, in fact, fell 10 percent in February from January and is down 27 percent from a year ago to the lowest total since December 2006, according to a new report from RealtyTrac.
(Read more: Foreclosure falls to lowest in 7 years: Report)
"Cold weather and a short month certainly contributed to a seasonal drop in foreclosure activity in February, but the reality is that new activity is no longer the biggest threat to the housing market when it comes to foreclosures," said Daren Blomquist, vice president at RealtyTrac.
(Read more: Google to invest $50 million in real estate site Auction.com)
The report, however, does note that more than 152,000 properties that are in the foreclosure process but not yet bank-owned have been vacated by their former owners, likely due to the long foreclosure timelines. These so-called "zombie foreclosures" have been in process an average of 1,031 days, according to RealtyTrac. These homes sit untended and are a blight to the neighborhoods around them, often reducing nearby property values.