The Reds have won just three of their opening eight top flight games and trail leaders Manchester City by nine points, barely a quarter of the way through the campaign.
Jurgen Klopp's men have now won just one of their last five league games and are struggling at both ends of the field with the goals having dried up since the 4-0 demolition of Arsenal in August, while defensively there remains major concerns.
And Heskey believes as many as five new additions are needed for Liverpool to be taken seriously as possible title contenders.
"Liverpool would need to do a lot in the transfer market to win the Premier League," he told sportingbet.com. "It will take a sustained effort in numerous transfer windows to make the necessary signings; it's not a quick fix.
"I think Liverpool would need to sign four or five players, with the priority being to improve the defence and the goalkeeper.
"The club would also need to sign a defensive midfielder, I still don't think they've replaced Dietmar Hamann and he left over a decade ago. Lucas played there for a while and did well, but it has been a struggle and I don't think they've got it right."
Though four new players did arrive at Anfield during the summer transfer window, Klopp was unable to complete a deal for Virgil van Dijk who, despite handing in a transfer request and being forced to train away from the first team, remains at Southampton.
Barcelona have since been linked with a move for the Netherlands international in a deal worth £50m (€56m), but having ended the summer empty-handed Liverpool should have prepped better says Heskey.
"Van Dijk was the one and we took our eye off the ball," he added. "Van Dijk has proven what he can do and he would suit Liverpool no doubt about it, but it shouldn't have just been him.
"Liverpool should have had a shortlist of options but they appear to have put all of their eggs in one basket. When that fell through they felt they had to move on and stick with what they had.
"Klopp, as with all managers, clearly felt he had to back the players he has at his disposal and now they need to show they're good enough."