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The highly rated centre-back was part of the France team that defeated Russia at the European Under-21 Championship on Sunday, a much-needed result after they had lost their opener at the tournament.
There was no rest for Konate, however, as stories circulated that Liverpool are hoping to wrap up his signing ahead of next season.
The Athletic detailed how the Premier League champion has made "significant progress" in its pursuit of the 21-year-old, who is said to have a €40million release clause.
Konate, though, is only focused on the remainder of the season, despite the speculation surrounding his future.
"I woke up, I saw my phone ringing all over the place, I just wanted to tell them: 'Hey, I played yesterday, I'm tired, leave me alone'," he said, according to quotes in L'Equipe.
"We can't focus on that, there is the Euros and then the return to my club. You have to focus on that, not on the external things."
A move for Konate – who has not committed an error that led to a shot in any of his 15 games for Leipzig this season – would help add depth at what has become a problem position for the Reds.
The former Sochaux player has won 64.7 per cent of his duels in nine Bundesliga games in 2020-21, as well as completing 83.5 per cent of his attempted passes. Injuries have restricted his appearances, though, and he did not feature in the Champions League last-16 tie against Liverpool.
Jurgen Klopp has been without the services of Virgil van Dijk and Joe Gomez for much of Liverpool's title defence, while Joel Matip is also a long-term absentee.
Ozan Kabak – who joined on loan from Schalke in a deal that includes an option to buy the Turkey international - and Ben Davies arrived in the mid-season transfer window to help provide further defensive options, though the latter has still yet to feature following his move from Preston North End.
Nathaniel Phillips and Rhys Williams have had unexpected first-team opportunities due to key absentees, while Klopp has also utilised midfielders Fabinho and Jordan Henderson as makeshift options at the heart of his back four.
Konate's arrival would help strengthen a defensive unit that has understandably struggled this term, conceding 36 goals in 29 Premier League games.
Liverpool sits in seventh place in the table as it prepare to return to action after the international break with a trip to Arsenal on Sunday (AEDT).