The Reds signed the midfielder from Fulham for a transfer fee of £1.53 million back in the summer of 2019.
Elliott averaged a WhoScored player rating of 6.95 in Liverpool's opening four matches of the season.
According to Jones, Klopp and his staff have been delighted by the Englishman's development in recent times.
"Liverpool may well decide to change tack and delve into the transfer market before the window closes on Thursday, but they’ll do well to find a player with more to offer, or with greater potential, than Elliott," he told GOAL, as quoted by Anfield Watch's Twitter account.
"Klopp and his staff have been blown away by his development over the past 12 months, and know that he is a player for the here and now as well as the future. Privately, some at Anfield believe he has an outside chance of making England’s World Cup squad.
"It has been interesting, to say the least, to see Elliott’s development tactically at Liverpool. He arrived as a wide player, a dribbler and a creator from the right flank, but it is apparent that Klopp sees his future in the centre."
Jurgen Klopp's pre-match press conference starts in just over two hours.
Will there be any more news on potential midfield plans? 🤔 pic.twitter.com/wxEFGPUdAn
Anfield Watch Verdict
Elliott is such a fine talent. The 19-year-old's development was halted last season.
Elliott suffered a serious ankle injury against Leeds United at Elland Road back in October 2021.
As a result, the Englishman missed a total of 30 games for Liverpool's first-team last season.
But, Elliott is fit and firing once again. We wish the youngster all the best for the remainder of the season.