The Scot has made just nine starts in the past two seasons for the Old Trafford outfit, having seen his participation limited by an ongoing battle with ulcerative colitis that forced him to recently undergo surgery.
When asked to put a date on his return, Fletcher told BBC Radio 5 Live: "Hopefully, not too long after the start of the season. I think I will just miss the beginning of the season."
The 29-year-old also underlined the importance of going under the knife to his long-term health prospects and spoke encouragingly about his prognosis ahead of a potential return to the field.
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"Medication wasn't helping me but surgery was the only solution if I wanted to have not only a future playing football but even a quality of life going forward.
"It's all going well. I am still under the hands of the medical team just now and the surgeon who is looking after me. Everything is going to plan so far and I am not that far away now.
"I am doing exercise on my own. I've not been given the green light to join in contact in football training but I am doing my own running and physical activities and feel great.
"Hopefully, in the next few weeks I am going to get the green light to join in and to start making the comeback, which is looking very good."
Fletcher has made over 300 appearances for United, winning five Premier League titles and one Champions League during that time.