The 34-year old has been offered an initial one-year deal with the option of a second by Clarets boss Brian Laws but he rejected the offer.
Laws was disappointed the Blake had showed his intentions to leave the club but said that the door would be left ajar if he were to change his mind.
"Obviously I am disappointed that Robbie has turned down what we consider to be a very reasonable deal for a 34-year-old," Laws told the club's official website. "The offer is a 12-month deal with a further one year option but Robbie wanted two years and we just couldn't go down that road.
"We included the extended deal should Robbie play 20 games next season and I feel a fit Robbie would have easily achieved that. So naturally I am disappointed, but would like to thank Robbie for all his magnificent service for the club.
"I know he is a firm fans' favourite and he is rightly considered a legend here, who will never be forgotten. But I have told Robbie and his agent that we have left the door open and if he has a change of mind I would be more than happy to talk."