According to reports by the Associated Press and ESPN.com, Howard recently told reporters that Parsons' departure won't affect the team's run for a title.
"It won't affect us at all," Howard said. "We have myself and James. We have the best center and the best two guard in the game on the same team. It's on us."
Howard was speaking at his father's 10th annual basketball camp in Atlanta when he made the comments about Houston's 2015 season.
In a busy yet somewhat unproductive offseason, the Rockets tried unsuccessfully to sign Carmelo Anthony before chasing Chris Bosh.
Houston settled for Trevor Ariza, who has already spent time in a Rockets jersey.
But Howard, who was teammates with Ariza when he played in Orlando, believes signing the veteran forward is a great move for the team.
"He'll go through a wall for you," Howard said. "Just to have soldiers on your team like that is great. We have that one-two punch with me and James. We're filling out our roster with guys who are willing to go through that wall and doing whatever it takes to win."
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Denton Ramsey may be reached via email at TXSWReport@gmail.com