The 27-year-old has played for the Red Devils for nine seasons, counting the current campaign.
He is eligible for a testimonial when he reaches ten years.
But The Athletic claims that Jones rejected that chance.
Jones reportedly said that other than his parents, he was not sure if anyone would turn up.
It is no doubt that Jones has become some sort of a lightning rod for criticism among United fans for his performances in the past few years.
Many were unhappy at him being rewarded with a new four year deal near the end of last season.