Neither Cornrich nor O'Brien could be reached for comment. Penn State spokesman Jeff Nelson said he had no information on whether talks had taken place.
After reports Saturday about O'Brien's future, one of his top recruits, defensive tackle Thomas Holley of Brooklyn, N.Y., said O'Brien told him he was staying at Penn State.
"I just got off the phone with him," Holley told 247Sports.com, a recruiting website. "He said he isn't going. [The report] isn't true."
Should O'Brien leave in the next weeks for the Texans or another NFL team, a list of candidates to replace him probably would include Tennessee Titans coach and former Penn State star Mike Munchak; ex-Nittany Lions assistant and Tampa Bay head coach Greg Schiano; and Vanderbilt head coach James Franklin, who grew up in Bucks County.
In the Texans' talk with O'Brien, the Houston Chronicle reported that the team was represented by chairman Bob McNair, vice chairman Cal McNair, and general manager Rick Smith.
Bob McNair acknowledged to the Chronicle that O'Brien was the leading candidate but said, "The process continues. We have other interviews scheduled [this] week. This isn't over."
The Texans also have interviewed interim coach Wade Phillips and former Chicago Bears head coach Lovie Smith, the Chronicle reported.
Gary Kubiak was fired as Houston's head coach on Dec. 6, replaced on an interim basis by Phillips. The Texans are 2-13. If Houston loses to the Titans on Sunday, it will receive the No. 1 overall pick in the 2014 NFL draft.
Bob McNair told the Chronicle he wants someone who has been a head coach and has NFL experience. O'Brien fits both descriptions, having led Penn State to records of 8-4 and 7-5 the last two seasons after going there following five seasons with the New England Patriots, the last as offensive coordinator.
After renegotiating his contract last spring, O'Brien's buyout to leave Penn State for an NFL job is approximately $6.7 million.
Presumably, the buyout would be covered by his new employer. ESPN reported last week that O'Brien's representatives were seeking to have the buyout reduced further.