The 29-year-olds existing deal is due to expire at the end of the season but the Jurgen Klopp now wants the club to offer him fresh terms following a bright start to the season.
Sturridges four goals in nine appearances so far, including two in a week against Chelsea, has seen him force his way into the Liverpool managers plans for the season.
According to The Sun, Liverpool will offer the striker an extension on his current £140,000-a-week contract with the deal set to be structured on his appearances following consistent injury issues in recent seasons.
The player himself has confirmed his intention to remain at Liverpool at least until the end of the season amid suggestions he would leave the club in January.
He told the clubs official website: Im always trying to push myself to the next level and contribute as best I can to the team to allow us to be successful.
Its important to stay focused throughout the season to get to the end – and hopefully have something to be excited about at the end.
Sturridge will be in contention to play against Huddersfield this weekend following an injury to Sadio Mane on international duty with Senegal.