The fly-half was expected to miss the game after he tore a tendon in his biceps while still playing for Auckland-based Super 15 club the Blues in May.
Noakes, 28, is expected to touch down in England next week, and Exiles director of rugby Brian Smith is certain that the Kiwi will be involved.
"It's quite a common injury," Smith is quoted as saying by Get Reading. "There are players who have snapped biceps and haven't repaired them, but he's a young man and wants to have full functionality.
"We had plenty of time and chose to have it repaired. It's not a big issue so he'll be back in light training initially and, start properly from the beginning of August.
"We're expecting he'll be fit and available for the first game."
Irish come up against Harlequins on September 6 at Twickenham.