Barnsley boss Andy Ritchie said: "We're very pleased with Richard, he's on the schedule we set."
Tykes physio Rick Holden added: "Richard has a programme to follow and we are very happy with how he is coming along."
Kell will miss his side's eagerly-awaited trip to Glanford Park on August 9, though the midfielder may be fit to face his former club at Oakwell on December 10.