AceShowbiz -

Sources have reported that they saw Blake Lively and Ryan Reynolds hunting for a house in New York. The "Green Lantern" co-stars never confirm that they are dating but if the report is true, then their relationship is moving at a light speed.

Lively has been frequently seen with Reynolds since her split from actor Leonardo DiCaprio earlier this year. She was his companion on his birthday last month. They have been seeing each other for about a month now and may be looking at a future together.

Among the properties they saw was a $4.5 million apartment in Manhattan. It is sandwiched between the historic Flatiron building and the Empire State and is nestled on the back of Madison Square Park. "When they'd finished looking Blake left the building first. She was wearing knee-high boots with jeans a coat and a fedora hat," a witness said.

The couple apparently is still discreet about being seen together, stepping into the same car at a time difference. "Blake's little dog was waiting with the driver in the car for them while they looked inside the building," the witness added.