Klopp is already battling to hold off Brazilian playmaker Philippe Coutinho, with Barcelona not giving up the chase despite having a £72m bid rejected.
The Liverpool boss has insisted Coutinho is not for sale as he continues to put together a side he believes is capable of challenging for the Premier League title this season.
But Express Sport understands Klopp could soon have a battle on his hands to keep another of his key players – Sadio Mane – at the club.
Inter Milan, who have had Mane in their sights for some time, are now ready to make a move for the Senegal international.
Mane made a comeback from injury during the Reds’ 3-0 friendly win against Hertha Berlin at the weekend and Inter are now understood to be preparing a £35m bid.
Liverpool would likely baulk at being offered a similar figure for a player they bought only 12 months ago, given Mane’s impressive form last season and the current inflated transfer market.
The 25-year-old scored 13 goals last year despite missing the end of last season with a knee ligament injury.
Mane has caught the attention of Inter who are keen to bolster their ranks to compete with local rivals AC Milan who have spent around £150m this summer.
Erick Thohir, Inter’s Indonesian businessman, has bankrolled the arrival of four players so far with £20m arrival defender Milan Skriniar from Sampdoria their biggest outlay.
The Serie A giants want Mane to be their marquee signing but the player is focused on returning to form with Liverpool.
“I’m very happy to be back,” he said today. “It was not easy to be off the pitch for three months. But finally, I’m back and I’m happy to be back.
“I’m looking forward to the season. I’m a professional and every football player would like to play each week. I want to always help my team-mates on the pitch and help my club to get better.
“[I want] to score more goals for my team and to assist as well. Why not win trophies with the team? I’m very confident and looking forward to it.
“There are still some things to work on. That’s why I’m training all the time. It will come. I’m not 100 per cent fit but it’s pre-season so I’m OK with that. It will come.”