And Laws has confirmed the Owls have made an improved offer to Port Vale for Sodje's brother Akpo.
Laws told BBC Radio Sheffield: "We're awaiting Vale's response to our bid.
"I spoke to (Reading manager) Steve Coppell over the weekend, and we've sorted some issues that will allow Sam to join us."
Laws added: "Were also waiting for Vale's response, but we can't increase the bid any further.
"Akpo was a real handful against us in pre-season. Maybe that's what we're missing at the moment - someone who can be a real physical presence for us."