The 30-year-old must now agree personal terms and pass a medical before a deal can be completed.
Lucas is Liverpool's longest-serving player, having joined the club for £5m in July 2007 from Gremio.
He made his international debut for Brazil later that year and has gone on to win 24 caps for the five-time World Cup winners.
After Liverpool's final match of the season, a 3-0 win over Middlesbrough, Lucas was presented with a commemorative trophy by Kenny Dalglish to mark his decade with the club.
"It's been an incredible 10 years, we all know it's been a little bit like a rollercoaster: a lot of ups and downs," he said, after receiving the trophy.
"But I'm so proud to wear this shirt every day of my life.
"This club made me better as a person, as a player, I have two kids born in Liverpool.
"I don't have one specific moment I'd say was a highlight, I think these 10 years have been a very good 10 years."
Lucas made 31 appearances for Liverpool last season, 24 of which came in the Premier League, and he scored one goal.
In 10 seasons, Lucas has played 247 times for Liverpool in the Premier League, scoring once and contributing 14 assists.