Archie averaged 10.9 points and 6.4 rebounds a game for the Gamecocks last season.
He said he received valuable feedback about his game from his workouts for NBA teams, but believed it was in his best interest to stay in school.
A source close to the program said that junior guard Devan Downey, the team's leading scorer at 19.8 points and 4.5 assists a game, will make a decision after another workout scheduled for Thursday at Milwaukee. The deadline to withdraw from the NBA draft is Monday.
South Carolina missed out on the NCAA tournament after finishing 10-6 in the SEC. The Gamecocks, under first-year coach Darrin Horn, were 21-10 and lost to Davidson in the postseason NIT.
Getting Downey and Archie back is critical to the Gamecocks keeping pace in the rugged SEC East with Kentucky, Tennessee, Florida and Vanderbilt next season.
Andy Katz is a senior writer for ESPN.com. Information from The Associated Press was used in this report.