Preston North End have also registered an interest in the player.
Manager Nigel Adkins and chairman Steve Wharton met with the player and his agent on Tuesday, and offered him an improved contract to stay at Glanford Park.
"It is still early days, Billy and his agent are well aware that we want him to stay," Adkins told the official SUFC website.
"He is hot property, but he is our player and we want him to stay at our club.
"Sharp will not leave unless there is a move that is right for him and Scunthorpe United are reimbursed accordingly."