The Hoops snatched the Scottish Premiership title away from Hearts on the final day with a dramatic 3-1 victory at Celtic Park.
Celtic also beat Dunfermline in the Scottish Cup final, securing a domestic double in May, with excitement building this summer.
O'Neil is set to make several changes to his squad after his side made hard work of winning the title, as the veteran boss was credited with an incredible turnaround.
Hearts were nailed on to win their first Scottish title for the first time in 66 years, but O'Neil masterminded a recovery after Wilfried Nancy's disastrous tenure, and now Chris Sutton has urged the board to invest this summer.
"Martin worked wonders last season," Sutton told Sky Sports.
"I didn't see Celtic winning the title from the position which he was put in on a couple of occasions. The run towards the end of the season was extraordinary.
"You can't get away from the fact there needs to be a lot of change at Celtic in terms of recruitment. So Martin will be looking to, I'm sure, bring players in.
"It'll be interesting to see who goes out from Celtic. It looks Reo Hatate will go, possibly Daizen Maeda and Arne Engels but they're big players for the team.
"So who is Celtic going to replace those type of players with? I think that Celtic are possibly going to have to spend up to or more than £50m really because the squad does need a rebuild."