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Bobbi Kristina Brown

Kevin Mazur/WireImage via ABC

Bobby Brown and his family are not giving up hope!

As Bobbi Kristina Brown begins her third week in a Georgia hospital, those closest to her are remaining positive about a recovery.

In fact, despite reports that Whitney Houston's daughter will be taken off life support this week, Brown's attorney Christopher Brown says those rumors are simply not true.

Those are "false stories," he revealed to E! News Monday morning before assuring the media that there is "nothing happening."

Since Bobbi Kristina was hospitalized on Jan. 31 after being found facedown in a bathtub full of water at her home, there have been a variety of reports about her progress or lack thereof.

Bobby Brown, Bobbi Kristina Brown

Ron Galella, Ltd./WireImage

Some insist the 21-year-old is showing improvement while others caution that doctors have not been the most optimistic. Regardless of all the stories out in the media, Bobby wants people to focus on praying for a recovery.

"We continue to request privacy in this matter," he said in a statement to E! News just this past Friday. "We thank everyone that supports Bobbi Kristina and God is healing our prayers."

One of the many fans around the world hoping for a recovery is Kevin Costner.

Three years after the 60-year-old actor gave a touching eulogy at the funeral of Houston, Costner says he sincerely hopes Bobbi Kristina's fate isn't nearly as tragic.

"My thoughts are probably similar to everyone, which is obviously, the similarities, what's going on, the worry that this might have happened again," he told Nightline. "Where is this little girl going to go when you lose your mother?"

He added, "I hope that God opens her eyes and lets her breathe and lets her brain work, and she gets a second chance."

—Reporting by Holly Passalaqua