The homegrown 22-year-old has been in good form for the Reds this season, and has grown into a role as one of Jurgen Klopp's most valuable midfielders, when available.
Jones has shone particularly in recent outings, scoring twice in the 5-1 Carabao Cup quarter final win over West Ham and netting in the 4-2 Premier League win over Newcastle on New Year's Day.
The midfielder, who also played a key role in England's Under-21 European Championships last summer, has already made over 100 first-team Liverpool appearances since his debut during the 2018/19 season.
Anfield Watch has been told that although Jones' current deal does not expire until 2027, Liverpool are prepared to offer a contract extension with improved terms, taking his stay at Anfield until 2029.
Jones, who joined the Reds' academy at the age of nine and has captained the first team on two occasions, is understood to be one of the Reds' lowest-paid senior players currently.
Some recent reports claimed that Arsenal were looking at the Liverpool No. 17 ahead of a possible summer move, though Anfield Watch understands this is wide of the mark and the Reds are unaware of any serious interest.
Earlier this season, Liverpool assistant manager Pep Lijnders hailed Jones' 'Scouse mentality', while Klopp heaped praise on the midfielder after his display against Newcastle.
"Special game, special game from Curtis, to be honest. His high press, his counter-press," the manager said.
"We all know how good a player Curtis is, he’s technically incredibly skilled, but he finds more and more direction in his dribbling, he gets better out of situations.
"And his pressing, counter-pressing, meanwhile, he sets the level, actually, how it should look.
"I’m really happy with that. It keeps every player in the game."