The former Rangers centre-back missed the League One run-in after breaking his kneecap in the 2-2 draw with Huddersfield.
But after a recent scan the 27-year-old has been given the green light to step up his rehabilitation.
"The aim is to be fit for the start of the season," Reid told the Colchester Gazette.
"I have a lot of work to do over pre-season to make sure that I'm in decent shape.
"I've been able to start slow jogging and swimming now, although I can't do any intensive jogging at the moment."