Both 35-year-olds are out of contract in the summer but gaffer Derek McInnes is keen to keep the experienced pair.
McInnes has already sounded them out on their futures and a pair of contracts will be slapped in front of the experienced Reds sometime in the coming weeks.
Anderson skippered the Dons to their first trophy in 19 years last month, and Robson has been a key component in the Aberdeen engine room since arriving last summer.
McInnes said: "I've spoken to Russell and Barry. They are well aware of how I feel and we'll get round to new contracts in due course.
"Barry and Russell have been great for us, they are our experienced players and they are the right type.
"Having guys like them goes a long way because they are top pros and know what's required."