Krychowiak won much praise for his performances last season and has been linked to moves to Germany and England, but Caillot said that he has not entertained the idea of the player's leaving Reims.
"At no time have we considered the possibility of letting Grzegorz go," Ligue1.com quotes Caillot as saying. "Once the technical staff had decided to keep him on, the matter was closed.
"His representatives have made me aware of half a dozen offers, notably from Fulham, who are very keen. I simply repeated the club's position to them - the player will stay on for at least one more season.
"We're still leaning towards extending his deal, and we're looking at a revaluation of the terms of his contract."
Lyon have also been credited with an interest in the player.