The Portugal international has been a revelation since signing from Wolverhampton Wanderers in 2020, contributing 34 goals and nine assists from his 85 appearances in all competitions.
With Sadio Mane having departed for Bayern Munich earlier this summer, the 25-year-old is expected to become more of a mainstay in Jurgen Klopp's starting lineup.
At a time when three years are still remaining on his contract, Liverpool do not necessarily have to be in a rush to enter contract negotiations with the player's representatives.
Nevertheless, according to CBS Sports journalist Ben Jacobs, club officials are now making every effort to agree fresh terms.
The Merseyside giants are said to be 'accelerating' discussions with the relevant people in order to keep Jota tied to the club past 2025.
If Liverpool are successful, it would follow on from Mohamed Salah having recently penned a new deal with last season's Premier League and Champions League runners-up.
The report has emerged at a time when Jota faces the prospect of playing catch-up in a bid to make an impact during the early weeks of 2022-23.
Earlier this week, Klopp revealed that the playmaker would be absent until at least the start of August after sustaining a hamstring injury.
Speaking to reporters, Klopp said: "Diogo, unlucky eh? He had an injury from the end of last season. He trained fully yesterday but got injured again. That's really not cool.
"Now we have to wait for the results. He had an assessment this morning so we will have to see. It's in the same area."
Liverpool remained well stock for options in the final third with Fabio Carvalho and Darwin Nunez having arrived from Fulham and Benfica respectively.
Klopp's side get their Premier League campaign underway with a fixture at the home of the former on August 6.