Robinson has spent five years at Saints, who were promoted back to the Guinness Premiership with Saturday's 18-8 victory over Exeter.
The 32-year-old, who has been linked with a move to Wasps, recently lost his place to Johnny Howard while Ben Foden's summer arrival from Sale will add further competition at nine.
"Mark is as popular as ever with the fans and I'm sure that there will be plenty of interest among other clubs in offering him a contract," said Saints director of rugby Jim Mallinder.
"But we have signed some exciting English qualified players at scrum-half for next season with a view to the longer term and competition for the starter's jersey will be fierce."
Robinson was voted player of the year by Northampton fans last season.