Richardson told Scott Powers of ESPNChicago: "I really believe that ... I really think we could be a NCAA team."
The Fighting Illini lost center Meyers Leonard to the NBA Draft and added new head coach John Groce in the off-season.
Last year, Illinois opened the season with a 15-3 mark before ending the season losing 12 of their last 14 games.
This year, the Illini's conference schedule will be equally difficult as they will have to play current No. 1 Indiana, No. 4 Ohio State, No. 5 Michigan, No. 14 Michigan State and No. 23 Wisconsin while also having No. 21 Gonzaga and No. 15 Missouri on its non-conference schedule.
In their three-year careers, Richardson and Paul have been to one NCAA tournament, one NIT tournament and are 58-44 overall but just 25-29 in conference play.