Gallas praised new signing Parker for his colossal contribution in midfield.
"I knew him from Chelsea," said the defender. "So I know what he can do. He does a good job for us. He sits in front of the two centre-backs. He runs everywhere. His quality is really good.
"He can make good passes and at the moment, yeah, he is one of the best midfielders in England."
Asked if reigning Player of the Year Parker could be the difference in the hunt for a top-four place, Gallas replied: "Maybe, maybe. We will see. It is not just down to him though.
"The squad is stronger this year and I think and believe we can do it, we can finish in the top four, maybe even win something.
"Everyone is talking about Manchester City, they did well. But I think we have to believe in ourselves and try to win every game and at the end of the season we will see."