Sam Allardyce's side were said to be preparing a bid for the 20-year-old earlier this week and were expected to close a deal during the January transfer window. But according to KentLive, Jurgen Klopp's men are now the favourites to seal a deal for Konsa as Charlton's owner Roland Duchatelet seeks to strip the London club of yet another asset, having already sold Ricky Holmes to Wigan Athletic for a paltry £400,000 this month.
Charlton manager Karl Robinson, a boyhood Liverpool supporter, is hoping that Konsa remains at The Valley until the end of the season as he looks to sustain his side's push for promotion back to the second tier of English football.
But Duchatelet, not exactly the most popular figure among Charlton fans, will no doubt decide to do what he sees fit with Konsa, who has become a mainstay in the centre of Robinson's defence this season.
Liverpool and Everton have pilfered two of Charlton's most promising youth graduates in recent seasons. The Reds signed centre-back Joe Gomez for around £3m in the summer of 2015, while Everton, who confirmed the signing of Theo Walcott from Arsenal earlier this week, signed attacker Ademola Lookman in a deal worth around £11m last January.
Everton have shown their intent to strengthen their youth ranks, most notably with the £6m signing of Newcastle United defender Lewis Gibson in the summer transfer window, but they now look set to miss out on a coveted to their bitter rivals Liverpool, who have already signed one centre-back this month in the form of Virgil van Dijk.
Konsa will likely start Charlton's home clash against Walsall on Saturday (20 January), but it remains to be seen if Robinson will be able to call upon the four-time England Under-20 international when the transfer window closes in 12 days' time.