"We have been through some dark days. However, the good news is that I am feeling better as each day passes and the consultant is hopeful that I will make a full recovery by next spring."
Cole, who won five Premier League winners' medals and the 1999 Champions League during his six years at Old Trafford, will continue in his role as a Manchester United ambassador.
He made his name at Newcastle United before joining Manchester United in 1995 and played 15 times for England.
Cole scored 187 Premier League goals during his career, joint second on the all-time list with Wayne Rooney behind former Blackburn Rovers and Newcastle striker Alan Shearer.
Meanwhile, former England and Arsenal defender Tony Adams has revealed he underwent life-saving heart surgery in Azerbaijan after complaining of chest pain.
Adams, 49, racked up 669 appearances and 10 major trophies with the Gunners before moving into management with Wycombe, Portsmouth and Azerbaijan-based Qabala.
Adams, who now serves as Qabala's director of football, recently underwent an operation after feeling unwell.
"After feeling some acute chest pain whilst exercising in Azerbaijan, and liaising with Qabala Club doctors, I went to The Medical Plaza Hospital in Baku where I was admitted for an angiogram, and then following diagnosis of a severely blocked vein, an immediate angioplasty," Adams said in a statement.
"The brilliant surgeons at the Medical Plaza did a fantastic job - as has been reiterated to me by my cardiologist in the UK.
"I know full well that without the brilliance of Dr Uzeyir Rahimov and his team I would not be alive now: a minor heart operation saved my life.
"I can't begin to thank Tale Heydarov and all at Qabala Football Club, as well as the Cardiac Unit at the Medical Plaza Baku enough."
Adams is now said to be recuperating back in the UK with his family.
- AAP
