He has 'opened negotiations' with the team now owned by an energy drink, Autosport claimed.
"His performances have been excellent this year," team principal Christian Horner told the magazine, "and he has been the perfect benchmark for the youngsters."
DC, the 34-year-old Scot and veteran of 182 grands prix, also confirmed his ambition to keep racing in blue overalls.
He said: "I'm absolutely thinking in terms of staying here."
It is also expected that Red Bull will have to chose between Christian Klien and Tonio Liuzzi for 2006, after sources reported that the current driver swapping will cease.