Skipper Wood, 23, and full-back Spurr, 21, both have a year left to run on their current deals but have yet to commit themselves to the club.
Chief executive Nick Parker told the Sheffield Star: "We're not a selling club, of course we want to keep all our best young players.
"We have a core of young really good players and around that I think what Brian Laws has been trying to do is bring in a bit of experience.
"Darren Purse, Tommy Miller and Michael Gray are slightly older, more experienced and a bit more level headed."
Parker added: "Brian has a budget and he knows he has to work within it. We have made offers to everybody we want to keep."