A decision on Wojcik's job status likely will be made before Friday, the source said.
Wojcik has been under investigation for the past few weeks.
Some players who had been on the team under former coach Bobby Cremins didn't react well to Wojcik's style, a source told Katz. Cremins was laid-back, and Wojcik, who played at the U.S. Naval Academy, has a much more rigid style. But there were no "Mike Rice-like" antics, the source said.
Rice, the former Rutgers coach, was fired by the university in 2013 after practice videos surfaced showing him shoving, kicking and berating players.
Attempts to reach Wojcik were unsuccessful Wednesday.
Wojcik finished the second year of a five-year contract and it is guaranteed. The school would have to determine if there is cause to fire him.
WCIV-TV in Charleston was the first to report that Wojcik was being investigated.
Wojcik, 50, is 38-29 in two seasons since arriving at Charleston. He has three years left on a five-year guaranteed deal that pays more than $400,000 per season.
Wojcik was previously the head coach at Tulsa, where he compiled a 140-92 mark in seven seasons. Wojcik was also an assistant for Tom Izzo at Michigan State and under Matt Doherty at both North Carolina and Notre Dame.
The College of Charleston hired a new president, former South Carolina Lt. Gov. Glenn McConnell, in April.
ESPN's Jeff Goodman contributed to this report.