The Cameroon international is recovering from a hamstring injury suffered in a first week of preseason.
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Onana told Sky Sports: "I feel good, I feel great.
"It's been a few difficult weeks but yeah, hopefully, I will be back for the start of the season. I'm enjoying the training with my guys and we are looking forward."
On United's chances of a successful season, Onana added: "If we have a good start against Arsenal, everything is possible."