Jurgen Klopp of the Reds are fighting on three fronts this season and have made an unbeatable start to their Premier League campaign.
They remain hunting to qualify for their Champions League group and will be among the favorites of the FA Cup when the third round is launched in the new year.
But despite their excellent start to the season, Liverpool still win every silverware under the Clop, which took them to three finals and lost them all.
However, former Reds striker Heskey – who has picked up the League Cup twice with Licester and four Cup in Liverpool – believes it is a matter of time until they win something expecting another cup once they do.
"I look at my time in Lester," he told Express Sports. "We reached three finals in four years – we won two of them and lost one.
"Success is a successful success … After you win one you want to get out there and win it again because you like the feeling ..
"You like to go to the cup finals having your family and friends there, and the fans call your name."
"You like to play in front of an audience of 75,000 or 80,000. Well, now it's 90,000.
"The moment they did that they would want to go out there and win more and more and more and more.The buzz is just something else.
Heskey was part of the Liverpool side that won a unique treble 2000-01.
Under Gerrard Houlier they played 62 games in the grueling season that yielded the FA Cup, League Cup and UEFA Cup.
And he believes the current crop of players has the same fighting qualities of the 2001 class and has backed them to go and match their success.
"I honestly do not remember much of the end of the season," he added.
"There were so many games but we had strength in depth even though we did not rotate much.
"We had a lot together and we knew how to watch games, especially in Europe.
"We would leave the place to be very solid and when we returned home we would say, 'You are not hitting us.'
"So we had this hunger, we had this struggle and this knowledge, we had the ability to win under the same circumstances.
"They (the side of the Clop) have the players with the ability and I think they have the players with a hungry fight.
Heskey is set to appear on a new gamehow and a different ball game will be introduced on the brand new online streaming platform SYNCR Live.
Sports fans will have the opportunity to challenge their favorite sports stars to a ball game.
And ski said: "My first love was athletics and especially runners.
"I loved practicing for it and it was the sport I wanted to do when I was young until I started playing football at age 8.
"I have also played some of the six sports that will be on another ball game while away with team members to international club matches, but I'm not going to say which only yet!"
To be with a chance to take part in the exhibition, head to the site of another ball game of sponsorship yourfreebet.com – the first bona fide site comparison site to the sports and casino sectors all in one convenient place) to rotate the wheel and you can play against Heskey, Paul Gascoigne, Robbie Fowler, Michael Owen or David Mark or Ray Prelor.