The 19-year-old troubled singer and Gazda, 18, were introduced at the end of last year by mutual friend Blake Kelly, reported Daily Mirror.
"They hit it off straight away and are both really serious about one another. But their relationship has been very up and down because she can't stand the way he has been behaving recently. She is desperately trying to help him through all the scandal and regain his clean-cut image.
"Underneath all the bravado and controversy, Katherine believes he's a lovely kid with a real heart, she just thinks he is being led astray," a source said.
On the other hand, many of Bieber's family fear Jeffries, 20, who has a criminal record, is a bad influence. The 'Baby' hitmaker was with the star on the night he was arrested for drag-racing while allegedly under the influence of drugs and alcohol.