The Reds have made a positive start to the Premier League season following a return of five victories to maintain a 100 per cent start.
Liverpool FC were 2-1 winners against title rivals Tottenham Hotspur at Wembley thanks to goals from Roberto Firmino and Georginio Wijnaldum.
The Merseyside outfit are sitting level on points with current leaders Chelsea FC to prompt talk of a genuine title challenge this term.
Klopp is still waiting to get his hands on his first piece of silverware as Liverpool FC manager following his appointment back in October 2015.
The Reds lost to Manchester City in the League Cup final in February 2016 before a 3-1 defeat by Sevilla in the Europa League showpiece months later.
Liverpool FC were on the wrong end of a 3-1 result in the Champions League final back in May as Real Madrid won the crown for the third successive season.
Former Liverpool FC striker Keane believes the Reds are destined for success under Klopp this season.
“There is no doubt in my mind that either this year or next year Liverpool will win the league, the FA Cup or Champions League,” Keane told Sky Sports.
“The stature of Liverpool means they want to win trophies. The fans demand it and the manager demands it more than anybody.”
Liverpool FC finished in fourth place in the Premier League in the last two seasons.
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