Cole believes Liverpool may regret not making at least one big-name signing this summer.
The former Reds midfielder told the Mirror: "Jurgen Klopp has done a great job. For him to take the team and take it to the next level - he's done an excellent job. He's great for the club and great for the league - everyone loves him.
"But I think he will be disappointed not to have brought in any major, marquee signings to add to his squad. If they're going to compete with Man City they need to kick on and go again.
"They were so close last year and Man City have strengthened. He's obviously happy with his players and he's going to have Lallana and Oxlade-Chamberlain back this year.
"But I think they need to go again if they're going to keep up with Man City because they seem relentless at the moment."