The Rockets will have three days to match the offer sheet.
The Rockets and Parsons negotiated throughout Tuesday and Wednesday, but were unable to come to an agreement on a deal, sources said.
It is unclear whether the Rockets will match the offer, but Houston general manager Daryl Morey has had conversations with the agents for the three best unrestricted free agent forwards: Luol Deng, Trevor Ariza and Paul Pierce, sources said.
The Rockets are prepared to give Chris Bosh a four-year, $88 million contract if he leaves the Miami Heat, but can't do that if they first match Parsons' offer sheet.
Parsons' agent Dan Fegan has Parsons and Dwight Howard as clients. If Houston matches, the two stars would be free agents together in 2017. Parson's offer sheet has a player option for the 2016-17 season, similar to Howard's contract.
Parsons has been one of the NBA's most underpaid players in his current deal, which was signed after Houston drafted him in the second round of the 2011 NBA draft. He averaged 16.6 points and 5.5 rebounds for the Rockets this season.
Parsons played a significant part in the recruitment of Howard to the Rockets and has expressed a strong desire to remain with the franchise.