Jurgen has already made moves to strengthen his Liverpool squad this summer by tabling a bid for Napoli forward Lorenzo Insigne.
The German is desperate to recruit the pacey 27-year-old forward as he looks to bolster his offensive options.
Liverpool are currently three points clear at the top of the Premier League but Klopp is aware that he must continue to improve his squad to maintain their progress.
Italian newspaper La Repubblica, via Sport Witness, are reporting that the Reds have launched a £61million offer for the Italian via his representative Mino Raiola.
Reports suggest the offer has been immediately rebuffed though by Napoli chief Aurelio De Laurentiis, who has told Liverpool to pay more than double their initial offer.
It is claimed Napoli will only accept an offer of £131m with Insigne tied to the club until the summer of 2022.
Insigne, who has earned 30 caps for Italy, has scored eight times and contributed five assists in 19 Serie A matches so far this season.
Liverpool have one of the most frightening attacking line-ups in world football but depth beyond Mohamed Salah, Roberto Firmino and Sadio Mane is sparse.
Klopp’s side surrendered another two points in the Premier League title race on Monday night following a 1-1 draw with West Ham.
It means reigning champions Manchester City are now just three points behind them following their convincing win over Arsenal on Sunday.