The winger has endured a difficult 12 months, with a hamstring injury suffered in training this time last year leading to a two-month absence, followed by a return which lasted two games.
A recurrence of the hamstring problem in November, followed by a further setback in the second half of last season, meant he didn’t feature again.
Months of intense rehabilitation saw Edwards get back to fitness, and he agreed a short-term deal until January earlier this month.
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Edwards made his return from an almost 10-month absence when he played the final nine minutes of United’s 2-1 defeat at Bristol City last time out.
He said: “That’s literally my goal, to get on the pitch and stay on the pitch. When January comes, if that’s me staying on again, and hopefully it is, then it’s me showing to the team and the fans, and everyone really, what I can do. That’s my plan.”
Edwards added: “I wasn’t even thinking of going anywhere else. The club stuck by me in a difficult time for me when they didn’t really have to.
“They put their hand out to me a lot of times, so I didn’t even think about going anywhere else. It was always to try and get back and play for Oxford.”