The 44-year-old, who won five Premier League titles with United between 1995 and 2001, has been treated at the Manchester Royal Infirmary over the past three weeks after being diagnosed with focal segmental glomerulosclerosis.
Cole's illness forced him to withdraw from the recent UNICEF charity match at Old Trafford and issue a statement explaining his absence to supporters.
"Fingers crossed, come spring or summer, but I've got a long way to go. I know it's going to be a tough battle but I know I'll get there," Cole told MUTV.
He added: "Not being able to do what I want and not being able to keep fit has been the toughest thing, I think.
"When you're fit, you take things for granted, like getting up in the morning and going for a run, stuff like that. I realise I can't do that anymore and it could be like that for the next four or five months."