Hamilton's initial 10-day contract expires Monday.
The shooting guard/small forward sustained a sprained right ankle in the third quarter of Sunday's loss to the Houston Rockets and sat out the rest of the game. Rivers said he's feeling better than expected.
"Hamilton is walking; there he is," said Rivers as Hamilton walked onto the court at the team's practice facility Monday. "He's better than we thought, so that's good."
Rivers, however, did not provide a timetable for his return.
Hamilton has averaged four points and 1.4 rebounds in 9.5 minutes over eight games.
Reserve guard Nate Robinson's 10-day contract expires Tuesday. When asked if the Clippers will re-sign him, Rivers seemed less certain than he was about Hamilton.
"We probably will, but I haven't clearly decided," Rivers said.
Robinson has averaged four points, 1.4 rebounds and two assists in 14.6 minutes a game over five games.
The Clippers need all of the help they can get while shooting guard Jamal Crawford remains sidelined with a deep right calf contusion. The reigning sixth man of the year has missed six straight games with the injury, and Rivers said Sunday that he's unsure whether Crawford will return before the playoffs.
"Jamal is out for a while," Rivers said Monday.