Richard Mithoff said he had contacted the Astros to inform them of the injury and to discuss options in the matter, the Houston Chronicle reported.
"The Astros' risk management representative reached out to the family, and now that the family is represented by counsel, I wanted to let the other side know that I am involved so that can get in touch with me," Mithoff said.
The unidentified girl was celebrating her birthday at the May 29 game against the Chicago Cubs when she was hit by a line drive off the bat of Cubs outfielder Albert Almora Jr. She was sitting along the third base line in Minute Maid Park when she was struck.
She suffered bleeding, edema and brain contusions from the ball's impact. She continues to suffer from seizures, Mithoff told the paper. Almora appeared to be shaken after the incident and was close to tears.
"Right now, obviously, I want to put a net around the whole stadium," he said after the game.
In a letter to Astros owner Jim Crane, Mithoff thanked the team for their interest in the girl's condition.
"I know Jim Crane and know him to be a responsible owner, and I think he will do the right thing," said Mithoff.
The injury comes after a series of similar incidents where fans where have been struck by high-speed foul balls. On Sunday, a girl in Dodger Stadium was hit by a foul ball off Dodgers outfielder Cody Bellinger. A woman died from a brain hemorrhage last year after she was struck by a foul ball in the same ballpark.
In 2017, a boy at Yankee Stadium was hit by a portion of Chris Carter's broken bat. That same year, a fan was hit by an Aaron Judge foul ball traveling at 105 mph.
In September, a 2-year-old girl was hospitalized from the impact of a 105 mph foul ball hit by then-Yankee Todd Frazier.
In 2018, all Major League Baseball teams extended netting past the home plate area to the far edge of each dugout to protect fans from foul balls. The girl in Houston was sitting 10 feet past the area where the netting ends.
Nine teams have placed additional netting beyond the dugout.
The Associated Press contributed to this report.