The 20-year-old Brazilian moved to Anfield from Inter Milan last week for a fee believed to be around £8.5m.
"He's a great talent - a young player but with a lot of experience - and I'm really looking forward to playing with him and helping him to settle quickly in England," Leiva told the club's official website.
"He doesn't speak much English, so I will try to be his dad for a few months and hopefully he will be okay.
"I've been here for a long time and it's just what I feel I need to do and what I feel I have to do. Hopefully he will feel comfortable."
Liverpool resume their Premier League duties on Monday when they host West Bromwich Albion.