Chairman Paul Baker told the Robins' official website: "We considered the offer to be a good one, but we're trying to build on the foundations of the last two seasons and we want to do everything we can to keep our best players.
"We were also mindful that Steven would prove a difficult player to replace even with a transfer fee at our disposal.
"The board therefore felt that turning down this offer was in the best interests of Cheltenham Town Football Club."