Konsa, part of the victorious England Under-20 World Cup side, has been linked with a move to the Premier League for many months after breaking into the south Londoners' first team last season.
Arsenal, Chelsea, Everton, Liverpool and Manchester United have all been linked with the 20-year-old, according to separate reports from The Evening Standard and The Mirror. But Charlton have refused to negotiate with the Premier League giants having lost a series of key players in recent years.
The Addicks have seen the likes of Rob Elliot, Carl Jenkinson, Joe Gomez and Ademola Lookman leave The Valley in the past six years but manager Karl Robinson now expects Konsa to join that list for a fee of around £5m.
"My gut feeling is that he [Konsa] will go in January," said Robinson at a meeting with supporters on Monday [13 November]. "If I was him I'd be looking to go in January but we should look for £5m minimum. Maybe we could try for a loan back [like Dele Alli] but the player has to want that."
After making his senior debut in the EFL Cup defeat to Cheltenham Town in September 2016, Konsa made his breakthrough in the 2016-17 season during which he made 39 appearances in all competitions.
Since returning from being part of the England side which won the Under-20 World Cup – a campaign in which he featured for just a single minute, coming on in the semi-final win over Italy – Konsa has made 16 appearances for his club primarily at centre-back, a position a host of top flight clubs including Arsenal and Liverpool are badly in need of improving.
Arsenal and Liverpool have both been urged to improve their defences ahead of the second half of the campaign and given their past dealings with Charlton a move to either The Emirates or Anfield could be in the offing for Konsa.
Robinson's side have enjoyed an encouraging start to the season in League One and are third in the table, seven points behind leaders Shrewsbury Town with a game in hand. Should Konsa indeed depart for the Premier League then Charlton will have money to spend in January, though a loan move for Arsenal youngster Eddie Nketiah has been derailed by his exploits for the Gunners first team.
"What happens in January will depend a lot on what happens with Ezri Konsa," he added. "It is like a jigsaw puzzle. We looked at Eddie Nketiah between the windows this year. Then he scored those two goals against Norwich. British based players are scouted by Steve Gallen. If a foreign player comes on the radar I'll consult with the regime in Belgium."