Beverley was ruled out for Wednesday's game against the Pelicans with torn ligaments in his left wrist.
Beverley visited with a doctor back in Houston on Wednesday and is getting a second opinion on his options, which could include surgery. Sources tell ESPN.com's Marc Stein that Beverley and the Rockets are holding out hope for a more favorable prognosis when the injury is re-evaluated.
Beverly has to wait for the swelling to subside to determine a possible course of action.
Beverley, who is averaging 10.1 points and 3.4 assists per game, was injured in a victory over the Indiana Pacers on Monday night.
Jason Terry and Pablo Prigioni will try to pick up the slack at point, with Terry moving into the starting lineup to replace Beverley.
Terry had two points and three assists in 27 minutes and Prigioni had two points and four assists in 20 minutes in Wednesday's 95-93 win over the Pelicans.
ESPN.com's Calvin Watkins and Marc Stein contributed to this report.
Beverley Could Need Wrist Surgery
ESPN Rockets reporter Calvin Watkins discusses the possibility that Houston could lose point guard Patrick Beverley to season-ending wrist surgery.