The 21-year-old took the captain's armband for the final few months of the League Two campaign after injuries to Matt Gill and then Garry Kenneth.
Former Exeter midfielder Gill is expected to return to the squad for the start of pre-season but Parkes says it would be "lovely" to skipper the side once more.
"I love being the captain," he told the Bristol Evening Post. "Leading a side was always something I've wanted to do and I can't thank the manager enough for letting me do it over the last five or six months.
"It would be lovely if I could carry on with the armband next season, because I think I have matured as a player because of it.
"I also want to be the one to really push the boys on for what will, hopefully, be a promotion challenge for us.
"The way we played over the second half of the season was of a promotion-winning standard and we need to come back flying and try to maintain that level of performance going into the new season."