Konsa has made 34 appearances in all competitions this season, and the defensive-minded player has already been described as "a Premier League player" by Robinson.
However, the Addicks boss is keen to keep Konsa at the club for at least another 12 months to avoid having to part ways with another of the team's stars after Ademola Lookman joined Everton in January.
The 36-year-old is quoted by LondonNewsOnline as saying: "I know there are Premier League clubs who would chase him. They have people coming to watch him every week.
"I'd love to keep him for another year – that's down to me, his agent and the club to try and see what's right for everybody. You can't always get the fairytale scenario, where you want to keep all the players to get us to where we want to go to.
"Whether you are Charlton, Milton Keynes, Millwall or Sheffield United – when you have outstanding players, like we did with Ademola Lookman, it can be impossible to keep hold of them in modern-day football. I'd love him to stay but we have to convince him about going this way."
Charlton currently sit in 16th place in the League One table, just six points above the relegation zone.