O'Brien met with the Texans this week after Christmas at his home in Cape Cod, resulting in intensified discussions they hope will culminate with a finalized contract, the sources said.
The Texans still have a short list of candidates in case talks break down with the Penn State coach, sources added.
The Texans had been doing due diligence on O'Brien, including his six-year stint with the New England Patriots. The feedback has been strong in his favor, sources said, which motivated Houston to commence negotiations to get a deal in place.
O'Brien, 44, just finished his second season at Penn State, where he was the Big Ten coach of the year in 2012, followed by a 7-5 season this year while playing with a freshman quarterback (Christian Hackenberg) and amid heavy sanctions placed on the Nittany Lions after the Jerry Sandusky scandal.
Read more on ESPN.com.