The Frenchman has often partnered Virgil van Dijk at the back when fully fit since joining from RB Leipzig in 2021, making 90 appearances in all tournaments and scoring three goals.
Konate played 37 times for the Merseyside giants across all competitions in the 2023-24 campaign, but towards the end of Jurgen Klopp's reign, Jarell Quansah was often favoured in defence.
Konate's selection frustration continued at Euro 2024, where he was expected to get the nod alongside Dayot Upamecano amid suggestions that Didier Deschamps was not overly keen on starting William Saliba.
However, a late change of heart from Deschamps saw him side with the Arsenal man, who justified his selection during France's run to the semi-finals, and Konate did not play a single minute at the tournament.
Slot concerned about Konate form, injuries?
The centre-back was included in the first XI for Liverpool's 3-0 win over Manchester United in the USA, but he was brought off at half time and was lambasted for his display at the back.
The 25-year-old is now back at Kirkby being put through his paces ahead of Sunday's friendly double-header with Sevilla and Las Palmas, and he will be expected to face the former in the day's lunchtime kickoff.
However, a report from Football Insider claims that Konate has not played his way into Slot's good books during the Dutchman's first few weeks at the club, for a variety of reasons.
The ex-Feyenoord boss has apparently highlighted Konate's injury record as a concern, as the France international, as he has missed 23 matches for club and country since joining Liverpool in 2021.
Such problems have supposedly raised 'red flags' in the Liverpool medical room, and an in-depth analysis of his performances in training and matches have also left a lot to be desired.
Konate is now in the last two years of his deal with Liverpool, and while there has been no talk of an extension, it is difficult to see the Reds sanctioning the Frenchman's sale in the coming weeks.
However, should the 25-year-old remain out of favour under Slot, a transfer is not entirely beyond the realm of possibility before he enters the final 12 months of his Reds contract.
Will Liverpool sign a new centre-back this summer?
Adding a new centre-back to the ranks was seemingly priority number one for Liverpool this summer, but the Reds are now focusing on bringing in a new number six, more specifically Real Sociedad's Martin Zubimendi.
Slot is still thought to be open to adding any affordable centre-backs to his ranks this summer, especially if no new deal can be agreed with Van Dijk, but Sepp van den Berg's emergence has lessened their need to dip into the market.
Van den Berg's future is still up in the air, though, while Nat Phillips, Joe Gomez and Rhys Williams are being linked with exits too, but any defensive arrivals will hinge on exits in the closing stages of the window.