Although they were written off as Premier League title contenders during the summer, Brendan Rodgers' side have started the campaign well, recording back-to-back victories over Stoke and Aston Villa.
Sturridge has been the match-winner on both occasions, proving he has fully recovered from the ankle injury that prevented him from being named in the England squad that defeated Scotland earlier this month.
And Jones knows the former Manchester City star will have to be watched closely.
"He is a cracking player," said Jones.
"He's one that we'll work on and watch out for."
New United boss David Moyes is guaranteed a hostile reception given his Everton background, not that Anfield is a warm environment for any United player.
"It's never easy going to Anfield, they put you under a lot of pressure," said Jones.
"It's going to be a big game for the players and manager.
"We'll have to go there and be at our best but I'm sure if we find that cutting edge we can get three points."
United will need to be more incisive than they were in last night's 0-0 draw with Chelsea, when their openings were severely restricted.
Yet Jones takes comfort from another excellent defensive display, which could end up being the foundation to a successful defence of their Premier League title.
"Wayne (Rooney) had a few long-range efforts and we could have had a penalty shout in the final 10 minutes for handball, but you win some, lose some with those," said Jones.
"We got the clean sheet and looked solid defensively as a unit - not just the back four but collectively it was sound.
"It was probably just in the final third where we didn't find the cutting edge."
Jones was also able to play through the discomfort of a back injury sustained in the first half when he tumbled over Ashley Cole.
"I landed awkwardly," he said.
"It was stiff for 20 or 30 minutes but I soldiered on."