The girl was hurt by a 105 mph drive off his bat into Yankee Stadium's lower deck behind third base on Wednesday, and was taken to a hospital for treatment. Frazier has been in contact with her father.
"We've been texting back and forth. He said she's doing a lot better," Frazier said Monday. "He said the hard stuff is behind now and hopefully she'll be getting out, hopefully today."
Frazier plans to meet with the family.
"The father has been very gracious -- enough to call me and text me back," Frazier said. "We've been having a really good relationship so far. I've still been praying for her every day and hoping for the best."
Major League Baseball issued recommendations for protective netting or screens in December 2015, encouraging teams to have it in place between the ends of the dugouts closest to home plate.
The New York Mets went beyond that at midseason this year, and Cincinnati, Colorado, Detroit and San Diego have said they intend to expand protective netting before next season. San Francisco said it anticipates doing the same.
The Yankees said last month they are "seriously exploring" additional netting for 2018.