The Houston Rockets are seriously pursuing unrestricted free-agent small forward Trevor Ariza, according to sources close to the situation, signaling that they are exploring their options for replacing Chandler Parsons.

The Rockets are chasing Trevor Ariza in case they cannot keep Chandler Parsons, sources say. Brian Spurlock/USA TODAY Sports

The Rockets, sources say, also pursued free agent Luol Deng but appear to have fallen out of contention for the former All-Star, with Miami said to be making progress in its recruitment of Deng after losing LeBron James on Friday.

The Rockets have until 11:59 p.m. Sunday to decide whether to exercise their right to match Parsons' three-year, $46 million offer sheet from the Dallas Mavericks.

A source told ESPNDallas.com earlier Friday that the Rockets planned to match the offer to Parsons after signing Chris Bosh. The Rockets spent the afternoon clearing salary cap space, including trading guard Jeremy Lin and a future first-round pick to the Los Angeles Lakers, in anticipation of signing Bosh to a near-max deal.

However, Bosh opted to stay in Miami on a five-year, $118 million max contract, sources confirmed to ESPN. The Rockets could only offer Bosh a four-year deal for a little more than $80 million in order to keep point guard Patrick Beverley and match the Mavs' offer to Parsons.

The Rockets must decide whether it's worth paying Parsons more than $15 million per season without accomplishing their goal of adding an All-Star power forward this summer. Ariza would be a less expensive alternative while still giving the Rockets, who are coming off a 54-win season, a chance to contend in the loaded Western Conference.

Ariza -- and Deng -- are also on the short list of the Mavs' targets if Houston opts to match the offer to Parsons, sources said. Deng is seeking a multiyear contract with a starting salary around $12 million, while Ariza is seeking a multiyear deal with a starting salary between $9 million and $11 million.

The Mavs also are maintaining contact with the agents of free agents Lance Stephenson, Paul Pierce and Shawn Marion, who played the last five seasons in Dallas. The Parsons offer sheet, which starts with a $14.7 million salary, accounts for the rest of the Mavs' cap space after the soon-to-be-official deals for Dirk Nowitzki and Devin Harris are done.

ESPNDallas.com's Tim MacMahon contributed to this report.